IPhO 2027

Problems, 1st round Recommended by Supported by Information and registration at www.ipho.info The problems of the 1st round in the selection competition for the International Physics Olympiad 2027 You already advance with 30 points. So, what are you waiting for? Problem 1 (10 points) Lifted off All aboard, cleared for take-off, and then it’s already underway. The diagram shows the measured values of the three acceleration sensors, recorded with the app “phyphox” during an airplane takeoff and subsequently smoothed, as a function of time. The airplane started rolling from a standstill and the smartphone lay on a seat. 1.a) State which of the graphs gives the acceleration in the direction of the runway. Using the data in the diagram, approximately determine the lift-off speed $v_{r}$ of the airplane during this takeoff procedure. All went well! For the fortunately rare case that, during the takeoff of a multi-engine airplane, a problem with one engine occurs, an abort speed $v_{1}$ is defined for safety reasons. If an engine fails at a speed $v \leq v_{1}$ , the takeoff is aborted; at $v > v_{1}$ the takeoff is continued despite the engine failure. The abort speed $v_{1}$ and the runway length must satisfy the following conditions:

i. The length of the runway must be sufficient to reach $v_{1}$ with all engines and then come to a stop again at maximum braking force without using thrust reversal.

ii. The length of the runway must be sufficient to reach $v_{1}$ with all engines and then, with one failed engine, continue to accelerate to the lift-off speed $v_{r}$ . Now consider an airplane of mass $m$ with two engines, each of which produces a thrust force $F_{T}$ . The braking system produces a constant braking force $F_{B}$ . Apart from the braking force $F_{B}$ , friction effects shall be neglected. 1.b) For conditions i. and ii., determine an expression for the minimum required runway length $s_{i}$ and $s_{ii}$ , respectively, as a function of the given parameters. For a particular choice of $v_{1}$ , the runway length minimally required to satisfy both conditions becomes minimal. 1.c) Determine this value of $v_{1}$ and the minimum runway length $s_{min}$ for a takeoff of an Airbus A320 with the values: $m = 75 t$ , $F_{T} = 118 kN$ , $F_{B} = 100 kN$ and $v_{r} = 75 m s^{- 1}$ .

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram, Energy Conservation Method Competenze: Experimental Data Analysis, Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.1

Problemi, primo round Recommended by Supportato da Informazione e registrazione At www.ipho.info I problemi del primo round nella selezione della competizione per l’Olimpiade Internazionale di Fisica 2027 Hai già 30 punti. Allora, cosa stai aspettando? Problema 1 (10 punti) Sulla scala Tutti a bordo, approvati per il decollo, e poi è già in corso. Il diagramma mostra i valori misurati dei tre sensori di accelerazione, registrati con l’app “phyphox” durante un decollo di un aereo e successivamente smidati, come funzione di tempo. L’aereo iniziò a rotolare da un punto di sosta e lo smartphone giaceva su un sedile. 1.a) Stato quale dei grafici dà l’accelerazione nella direzione della pista. Usando i dati del diagramma, approximately determine the lift-off speed $v_{r}$ of the aircraft during this takeoff procedure. Tutto va bene! Per il fortunatamente raro caso in cui, durante il decollo di un aereo multi-motore, si verifichi un problema con un motore, una velocità di abortito $v_{1}$ è definita per motivi di sicurezza. Se un motore fa failli a una velocità $v \leq v_{1}$ , il takeoff è abortito; a $v > v_{1}$ il takeoff è continuato nonostante il fallimento del motore. Il tasso di aborto $v_{1}$ e la lunghezza della pista devono soddisfare le seguenti condizioni:

i. La lunghezza della pista deve essere sufficiente per raggiungere $v_{1}$ con tutti i motori e quindi arrivare a un stop again a maximum braking force senza usare la reversal di spinta.

ii. La lunghezza della pista deve essere sufficiente per raggiungere $v_{1}$ con tutti i motori e quindi, con un motore fallito, continuare ad accelerare alla velocità di lift-off $v_{r}$ . Ora considerate un aereo di massa $m$ con due motori, ognuno dei quali produce una forza di spinta $F_{T}$ . The braking system produces a constant braking force $F_{B}$ . Se non è possibile, la forza di frenata $F_{B}$ deve essere negligente. 1.b) Per condizioni i. e ii., determinare un’espressione per la lunghezza minima richiesta di pista $s_{i}$ e $s_{ii}$ , rispettivamente, come funzione dei parametri dati. Per una particolare scelta di $v_{1}$ , la lunghezza minimale richiesta per soddisfare entrambe le condizioni diventa minima. 1.c) Determine this value of $v_{1}$ and the minimum runway length $s_{min}$ for a takeoff of an Airbus A320 with the values: $m = 75 t$ , $F_{T} = 118 kN$ , $F_{B} = 100 kN$ e $v_{r} = 75 m s^{- 1}$ .

Problems, first round Recommended by Supported by Information and registration The Commission has also adopted a number of recommendations. The problems of the 1st round in the selection competition for the International Physics Olympiad 2027 You’re already advancing with 30 points. So, what are you waiting for? The following points are added: Lifted off All aboard, cleared for takeoff, and then it’s already underway. The diagram shows the measured values of the three acceleration sensors, recorded with the app “phyphox” during an aircraft takeoff and subsequently smoothed, as a function of time. The plane started rolling from a standstill and the smartphone lay on a seat.

(a) State which of the graphs gives the acceleration in the direction of the runway. Using the data in the diagram, approximately determine the lift-off speed $v_{r}$ of the aircraft during this takeoff procedure. It all went well! For the fortunately rare case that, during the takeoff of a multi-engine aircraft, a problem with one engine occurs, an abort speed $v_{1}$ is defined for safety reasons. If an engine fails at a speed $v \leq v_{1}$ , the takeoff is aborted; at $v > v_{1}$ the takeoff is continued despite the engine failure. The abort speed $v_{1}$ and the runway length must satisfy the following conditions:

i. The length of the runway must be sufficient to reach $v_{1}$ with all engines and then come to a stop again at maximum braking force without using thrust reversal.

(b) For conditions i. and ii., determine an expression for the minimum required runway length $s_{i}$ and $s_{ii}$ , respectively, as a function of the given parameters. For a particular choice of $v_{1}$ , the runway length minimally required to satisfy both conditions becomes minimal. 1.c) Determine this value of $v_{1}$ and the minimum runway length $s_{min}$ for a takeoff of an Airbus A320 with the values: $m = 75 t$ , $F_{T} = 118 kN$ , $F_{B} = 100 kN$ and $v_{r} = 75 m s^{- 1}$ .

Problem 2 (10 points) Attracted By rubbing it on a wool sweater or a (synthetic) fur, the thin rubber membrane of a balloon can be charged electrostatically. The charged balloon can then, as shown in the picture, stick to a ceiling. In the following, consider a spherical balloon filled with air whose shell has a mass of $m = 2, 7 g$ and is charged homogeneously with a charge $q = - 4, 0 \cdot 1 0^{- 7} C$ . The balloon is held against the ceiling and remains stuck to it without falling down. 2.a) Explain qualitatively why the balloon sticks to the ceiling. For simplicity, assume that the ceiling is conducting and grounded apart from a thin insulating surface layer. 2.b) Inform yourself about the method of image charges. Using this method, sketch and justify the course of the electric field lines in the region between the balloon and the ceiling. 2.c) Determine the maximum radius $r_{max}$ to which the balloon may be inflated before it falls off the ceiling. When the electric field strength in air exceeds a critical value of about $3, 0 \cdot 1 0^{6} V m^{- 1}$ , an electric arc or spark discharge occurs and the air loses its insulating effect. When that happens, the balloon also breaks. 2.d) Determine the minimum radius $r_{min}$ that the balloon, now freely located in space, must at least have so that no spark discharge occurs. The problems are best hung directly next to the poster! Problems and further materials for download Graphs of the accelerations a measured for the three axes of the sensors during the takeoff procedure as a function of time t. The data are also available as a table on the IPhO website. Picture of a balloon stuck to the ceiling. 10 20 30 40 50 60 70 80 90 2 4 6 8 10 12 14 $t / s$ $a / m s^{- 2}$

Topic: Electrostatics Metodi: Coulomb’s Law, Electric Potential Method, Symmetry Argument Competenze: Physical Reasoning, Mathematical Modeling, Diagrammatic Reasoning Objects: Membrane Fonte: Testo (PDF) — p.2

Problema 2 (10 punti) Attraverso Sfruttando il pulsante di lana o una pelliccia sintetica, la membrana di gomma sottile di un pallone può essere caricata elettrostaticamente. Il pallone carico può quindi, come mostrato nella foto, aderire a un soffitto. In the following, considerate un pallone sferico pieno di aria il cui guscio ha una massa di $m = 2, 7 g$ e è caricato omogeneo con una carica $q = - 4, 0 \cdot 1 0^{- 7} C$ . Il pallone è tenuto contro il soffitto e rimane attaccato senza cadere. 2. (a) Spiegare qualitativamente perché il pallone si attacca al soffitto. Per semplicità, supponiamo che il soffitto sia conduttore e sia fondato separatamente da un sottile strato isolante di superficie. 2.b) Informati del metodo di carica dell’immagine. Usando questo metodo, schizzi e giustificare il corso delle linee di campo elettrico nella regione tra il pallone e il soffitto. 2.c) Determina il massimo raggio $r_{max}$ al quale il pallone può essere gonfiato prima che cade dal soffitto. Quando la forza del campo elettrico in aria supera un valore critico di circa $3, 0 \cdot 1 0^{6} V m^{- 1}$ , si verifica un’arc elettrica o una scarica e l’aria perde il suo effetto isolante. Quando succede, il pallone si spezza. 2.d) Determine il minimo raggio $r_{min}$ che il pallone, ora liberamente situato nello spazio, deve almeno avere in modo che non si verifichi alcuna scarica di scintilla. I problemi sono meglio affamato direttamente vicino a Il poster! Problemi e altri materiali per download Grafici delle accelerazioni a misurate per i tre assi dei sensori durante la procedura di takeoff come funzione di tempo t. I dati sono disponibili anche come una tabella sul sito IPhO. Immagine di un pallone attaccato al soffitto. 10 20 30 40 50 60 70 80 90 2 4 6 8 10 12 14 $t / s$ $a / m s^{- 2}$

Problem 2 (10 points) Attracted By rubbing it on a wool sweater or a (synthetic) fur, the thin rubber membrane of a balloon can be charged electrostatically. The charged balloon can then, as shown in the picture, stick to a ceiling. In the following, consider a spherical balloon filled with air whose shell has a mass of $m = 2, 7 g$ and is charged homogeneously with a charge $q = - 4, 0 \cdot 1 0^{- 7} C$ . The balloon is held against the ceiling and remains stuck to it without falling down. 2. (a) Explain qualitatively why the balloon sticks to the ceiling. For simplicity, assume that the ceiling is conducting and grounded apart from a thin insulating surface layer. 2. (b) Inform yourself about the method of image charges. Using this method, sketch and justify the course of the electric field lines in the region between the balloon and the ceiling. (c) Determine the maximum radius $r_{max}$ to which the balloon may be inflated before it falls off the ceiling. When the electric field strength in air exceeds a critical value of about $3, 0 \cdot 1 0^{6} V m^{- 1}$ , an electric arc or spark discharge occurs and the air loses its insulating effect. When that happens, the balloon also breaks. 2. (d) Determine the minimum radius $r_{min}$ that the balloon, now freely located in space, must at least have so that no spark discharge occurs. The problems Are best hung directly next to The poster! Problems and further materials for download Graphs of the accelerations a measured for the three axes of the sensors during the takeoff procedure as a function of time t. The data are also available as a table on the IPhO website. Picture of a balloon stuck to the ceiling. 10 20 30 40 50 60 70 80 90 2 4 6 8 10 12 14 $t / s$ $a / m s^{- 2}$

Problem 3 (10 points) Held in place Laser beams can be used to exert forces on microscopic particles. The operation of an optical tweezer, which is used for example in the study of biological systems, is based on this phenomenon. In 2018 Arthur Ashkin was awarded the Nobel Prize in Physics, among other things for his work on this technique. For particles that are significantly larger than the wavelength of the laser light used, the force effect can be understood through the refraction of light rays. Consider a transparent and fixed polymer sphere with radius $r = 12, 0 μ m$ and refractive index $n = 1, 40$ . A laser beam strikes the sphere, as sketched in the figure, at a distance $d = 6, 0 μ m$ from the indicated central axis. Assume that no light is reflected. 3.a) Draw the path of the laser beam as it passes through the polymer sphere and determine the angle $θ$ by which the laser beam is deflected from its original direction. Consider a photon of the laser beam with momentum magnitude $p$ that is deflected by the polymer sphere. Due to the refraction the momentum changes its direction, but the momentum magnitude is, to a very good approximation, conserved. 3.b) Determine the resulting changes of the momentum components along the original direction of propagation and perpendicular to it. The polymer sphere is now irradiated at the indicated location with a laser of wavelength $λ = 530 nm$ and a power of $P = 1, 0 W$ . 3.c) Determine the forces acting on the polymer sphere due to the refraction of the laser light, along the original direction of propagation and perpendicular to it.

Topic: Geometric Optics, Modern-Quantum Physics Metodi: Snell’s Law, Ray Tracing, Photon Energy Relation Competenze: Mathematical Modeling, Physical Reasoning, Diagrammatic Reasoning Objects: Sphere, Photon Fonte: Testo (PDF) — p.3

Problema 3 (10 punti) Eroe in posto I raggi laser possono essere usati per esercitare forze su particelle microscopiche. Il funzionamento di un pinzetto ottico, che viene utilizzato per esempio nello studio dei sistemi biologici, è basato su questo fenomeno. Nel 2018 Arthur Ashkin è stato premiato con il Premio Nobel di Fisica, tra le altre cose per il suo lavoro su questa tecnica. Per le particelle che sono significativamente più grandi della lunghezza d’onda della luce laser utilizzata, l’effetto di forza può essere compreso attraverso la refrazione dei raggi luminosi. Considerare una sfera polimerica trasparente e fissa con radius $r = 12, 0 μ m$ e indice refraettivo $n = 1, 40$ . Un fascio laser colpisce la sfera, come illustrato nella figura, a una distanza $d = 6, 0 μ m$ dall’asse centrale indicato. Supponiamo che non si rifletta luce. 3.a) Disegnare il percorso del fascio laser mentre passa attraverso la sfera polimerica e determinare l’angolo $θ$ da cui il fascio laser è deflected dalla sua direzione originale. Consider a photon of the laser beam with momentum magnitude $p$ that is deflected by the polymer sphere. A causa della refraczione, l’impulso cambia la sua direzione, ma la magnitudine dell’impulso è, ad una buona approssimazione, conservata. 3.b) Determina i risultati dei cambiamenti dei componenti di impulso lungo la direzione originale di propagazione e perpendicolare a essa. La sfera polimerica è ora irradiata alla posizione indicata con un laser di lunghezza d’onda $λ = 530 nm$ e una potenza di $P = 1, 0 W$ . 3.c) Determinare le forze che agiscono sulla sfera polimerica a causa della refrazione della luce laser, lungo la direzione originale di propagazione e perpendicolare a essa.

Problem 3 (10 points) Hero in place Laser beams can be used to exert forces on microscopic particles. The operation of an optical tweezer, which is used for example in the study of biological systems, is based on this phenomenon. In 2018, Arthur Ashkin was awarded the Nobel Prize in Physics, among other things for his work on this technique. For particles that are significantly larger than the wavelength of the laser light used, the force effect can be understood through the refraction of light rays. Consider a transparent and fixed polymer sphere with radius $r = 12, 0 μ m$ and refractive index $n = 1, 40$ . A laser beam strikes the sphere, as sketched in the figure, at a distance $d = 6, 0 μ m$ from the indicated central axis. Assume that no light is reflected. 3.a) Draw the path of the laser beam as it passes through the polymer sphere and determine the angle $θ$ by which the laser beam is deflected from its original direction. Consider a photon of the laser beam with momentum magnitude $p$ that is deflected by the polymer sphere. Because of the refraction, the momentum changes its direction, but the momentum magnitude is, to a very good approximation, conserved. 3.b) Determine the resulting changes of the momentum components along the original direction of propagation and perpendicular to it. The polymer sphere is now irradiated at the indicated location with a laser of wavelength $λ = 530 nm$ and a power of $P = 1, 0 W$ . 3.c) Determine the forces acting on the polymer sphere due to the refraction of the laser light, along the original direction of propagation and perpendicular to it.

Problem 4 (10 points) Emptied out Poke a small hole into the lower part of the side wall of a plastic bottle filled with water and not screwed shut. The water then runs out of the bottle in a jet, as in the adjacent photo. The shape of the water jet changes with the fill level of the water in the bottle. 4.a) Determine experimentally the speed $v$ at which the water jet exits the bottle. State how you proceed in determining $v$ and take measured values for at least 10 different values of the height $h$ of the water surface in the bottle above the hole. 4.b) Show that $v_{th} = 2 g h$ represents a theoretical upper bound for the outflow speed. 4.c) Produce a suitable graph to compare your measurement results with the theoretical upper bound. Assess how well the experimentally determined speeds match the theoretically expected maximum. 4.d) Name at least two physical reasons that may be responsible for possible deviations between the theoretical prediction and the experimental results. Justify qualitatively how these influence the results. Junior problem (10 points) Long line High-voltage lines are used to transport electrical energy over long distances. The sketch shows the cross-section of a simple high-voltage line. The inner conductor is a steel cable and the six conductors lying on the outside are made of aluminum. The diameter of each of the individual cables is $d = 1, 5 cm$ and the length of the high-voltage line is denoted by $L$ . The steel cable is important for the mechanical stability but is less well suited for electrical conduction, since the resistivity of steel, $ρ_{St} = 1, 5 \cdot 1 0^{- 7} Ω m$ , is significantly higher than that of aluminum, $ρ_{Al} = 2, 7 \cdot 1 0^{- 8} Ω m$ . Denote by $R$ the resistance of the high-voltage line. If the central steel cable is removed, this resistance increases by $Δ R = 6, 1 \cdot 1 0^{- 4} Ω$ . Determine the length $L$ of the high-voltage line. r n Laser beam d Steel Al Al Al Al Al Al d Sketch of the polymer sphere with laser beam. Cross-section sketch of a high-voltage line. Register now at www.ipho.info www.ipho.info for the competition! Physics at its peak at the PhysikOlympiade The PhysikOlympiade in Germany is for all students who enjoy physics and have a taste for tricky theoretical problems as well as exciting experiments. Apart from the actual competition, there are also great opportunities to deepen knowledge, to meet other people enthusiastic about physics, and to experience science together. The PhysikOlympiade in Germany is part of the ScienceOlympiaden, which are coordinated by the Leibniz Institute for Science and Mathematics Education in Kiel (IPN) in cooperation with the education ministries of the federal states and funded by the BMBFSFJ. For the best five, the competition leads after four rounds to the International Physics Olympiad (IPhO), which is held each year in a different country. The host country for the IPhO 2027 has not yet been determined. The entry with the 1st round In the 1st round of the PhysikOlympiade in Germany, the four problems on this problem sheet are to be solved alone and as homework by the beginning of September 2026. Participants who, after the summer holidays, are not yet in the second-to-last grade level can earn a points bonus with the junior problem. Further information on rules, procedure, and deadlines can be found at www.ipho.info. 1st round for the IPhO 2027 – the procedure at a glance 1 2 3 4 5 Correction phase Start 1 April 2026 September 2026 Teachers Students Beginning of the 1st round Reaching out to interested students Register & sign up Support with material & with questions Looking at the problems and collecting ideas Register & sign up Correcting based on the model solution Personal code to students Working on the problems of the 1st round Submission of the work Deadline 7 September *) Feedback on results in October Submission to the teacher Entering the results & submitting the work Deadline 25 September 1 2 3 4 5 Registration and working period April–beginning of September 2026 *) Teachers may also arrange other dates at their own discretion, as long as the deadline for reporting results on 25 September 2026 is met. What comes next? Whoever reaches at least 30 points in the 1st round is invited to the second round, which is written as an exam. After that follow, with the national and the final round, the third and fourth stages of the competition, each as week-long events at a research site in Germany. In every round there are materials for learning and training. In addition, a variety of offerings, such as the Orpheus seminars, provide opportunities to broaden one’s own horizons and to exchange ideas with other people enthusiastic about physics. Curious? Then join in! We wish all students and supervising teachers much success at the PhysikOlympiade and much fun with the problems! Questions? The team of the PhysikOlympiade at the IPN and the state representatives are happy to help. Contact for the competition management PhysikOlympiade $\cdot$ IPN Olshausenstr. 62 $\cdot$ 24118 Kiel ipho@scienceolympiaden.de 0431 880-5120 or -5387 The cover image was taken by the FotoAG of the student research center at the Werner-Heisenberg-Gymnasium in Heide. International

Physics Olympiad Contact for the state representatives The addresses of the state representatives, who coordinate the conduct of the first two rounds in the federal states, can be found at www.ipho.info.

Topic: Fluid Mechanics Metodi: Bernoulli’s Equation, Experimental Data Analysis, Graph Linearization Competenze: Experimental Data Analysis, Graph Linearization, Measurement & Instrumentation Objects: Container, Wire Fonte: Testo (PDF) — p.3

Problema 4 (10 punti) Emptied out Poke un piccolo buco nella parte inferiore del muro laterale di una bottiglia di plastica piena di acqua e non si chiude. L’acqua scorre quindi dalla bottiglia in un jet, come nella foto adiacente. La forma del jet d’acqua cambia con il livello di riempimento dell’acqua nella bottiglia. 4.a) Determina sperimentalmente la velocità $v$ a cui il jet d’acqua esce dalla bottiglia. State how you proceed in determining $v$ and take measured values for at least 10 different values of the height $h$ of the water surface in the bottle above the hole. 4.b) Mostra che $v_{th} = 2 g h$ rappresenta un limite superiore teorico per la velocità di uscita. 4.c) Produci un grafico adatto per confrontare i risultati delle tue misurazioni con il limite superiore teorico. Valuta come le velocità determinate sperimentalmente corrispondano al massimo teoricamente atteso. 4.d) Indicare almeno due ragioni fisiche che possono essere responsabili di possibili deviazioni tra la previsione teorica e i risultati sperimentali. Giustificare qualitativamente come questi influenzino i risultati. Problema minore (10 punti) Long line Le linee ad alta tensione sono utilizzate per trasportare energia elettrica su lunghe distanze. Lo sketch mostra la sezione trasversale di una linea semplice ad alta tensione. Il conduttore interno è un cavo di acciaio e i sei conduttori che si trovano all’esterno sono in alluminio. Il diametro di ciascun cavo individuale è $d = 1, 5 cm$ e la lunghezza della linea ad alta tensione è denotata da $L$ . Il cavo in acciaio è importante per la stabilità meccanica ma è meno adatto per la conduzione elettrica, poiché la resistività di acciaio, $ρ_{St} = 1, 5 \cdot 1 0^{- 7} Ω m$ , è significativamente superiore a quella di alluminio, $ρ_{Al} = 2, 7 \cdot 1 0^{- 8} Ω m$ . Denote by $R$ the resistance of the high-voltage line. Se il cavo centrale di acciaio viene rimosso, questa resistenza aumenta di $Δ R = 6, 1 \cdot 1 0^{- 4} Ω$ . Determine la lunghezza $L$ della linea ad alta tensione. r n Radiodiffusione d Fabbricazione di acciaio Al Al Al Al Al Al d Sketch della sfera polimerica con raggi laser. Sketch di sezione trasversale di una linea ad alta tensione. Registrare ora a www.ipho.info www.ipho.info per il La concorrenza! Physics at its peak at the PhysicsOlimpico La PhysicsOlympiade in Germania è per tutti gli studenti che amano la fisica e hanno un gusto per problemi teorici complicati e esperimenti eccitanti. Oltre alla concorrenza, ci sono anche grandi opportunità per approfondire le conoscenze, incontrare altre persone entusiaste della fisica e sperimentare la scienza insieme. La PhysicsOlympiade in Germania è parte delle ScienceOlympiades, coordinate dall’Istituto Leibniz per la Scienza e la Matematica di Kiel (IPN) in collaborazione con i ministeri dell’istruzione degli stati federali e finanziate dal BMBFSFJ. Per i migliori cinque, la competizione conduce dopo quattro round all’International Physics Olympiad (IPhO), che si tiene ogni anno in un paese diverso. Il paese ospite per l’IPhO 2027 non è ancora stato determinato. L’entrata con il primo round Nel primo round delle Olimpiadi di Fisica in Germania, i quattro problemi su questo foglio di problemi devono essere risolti da soli e come compiti per l’inizio di settembre 2026. I partecipanti che, dopo le vacanze estive, non sono ancora al secondo-to-last grade level possono guadagnare un bonus di punti con il problema junior. Ulteriori informazioni sulle regole, procedure e scadenze sono disponibili su www.ipho.info. 1st round for the IPhO 2027 the procedure at a glance 1 2 3 4 5 Fase di correzione Inizio 1 aprile 2026 Settembre 2026 Docenti Studenti Inizio del primo round Raggiungere studenti interessati Register & Sign up Support with material & with questions Guardando i problemi e raccogliendo idee Register & Sign up Correcting based on the model solution Codice personale a studenti Lavorare sui problemi del primo round Submission of the work Data di scadenza: 7 settembre Feedback on results in ottobre Submission to the teacher (Sottomessione al maestro) Entrare i risultati e inviare il lavoro Data di scadenza: 25 settembre 1 2 3 4 5 Registrazione e periodo di lavoro Aprile inizio di settembre 2026 I docenti possono anche organizzare altre date a loro discrezione, purché sia soddisfatto il deadline per la comunicazione dei risultati del 25 settembre 2026. Cosa succede dopo? Chi raggiunge almeno 30 punti nel primo round viene invitato al secondo round, che è scritto come un esame. Dopo di che seguono, con il round nazionale e la finale, la terza e la quarta fasi della competizione, ciascuna come eventi di una settimana in un sito di ricerca in Germania. In ogni round ci sono materiali per l’apprendimento e la formazione. Inoltre, una varietà di offerte, come i seminari Orpheus, offrono opportunità per ampliare i propri orizzonti e scambiare idee con altre persone entusiaste della fisica.

Curioso? Allora entra! Auguriamo a tutti gli studenti e agli insegnanti supervisioni molti successi alla fisicaOlimpiade e molto divertimento con i problemi! Domande? Il team della PhysicsOlympiade all’IPN e i rappresentanti dello stato sono felici di aiutarvi. Contact for the competition management FisicaOlimpiade $\cdot$ IPN Strada Olshausen. 62 $\cdot$ 24118 chil ipho@scienceolympiaden.de 0431 880-5120 or -5387 La copertina è stata scattata dal FotoAG del centro di ricerca studentesco della scuola superiore di Werner-Heisenberg a Heide. Internazionale

Olimpiada di fisica Contact for the state representatives Gli indirizzi dei rappresentanti statali che coordinano la condotta dei primi due round negli Stati federali possono essere trovati su www.ipho.info.

Problem 4 (10 points) Emptied out Poke a small hole into the lower part of the side wall of a plastic bottle filled with water and not screwed shut. The water then runs out of the bottle in a jet, as in the adjacent photo. The shape of the water jet changes with the fill level of the water in the bottle. 4. (a) Determine experimentally the speed $v$ at which the water jet exits the bottle. State how you proceed in determining $v$ and take measured values for at least 10 different values of the height $h$ of the water surface in the bottle above the hole. 4.b) Show that $v_{th} = 2 g h$ represents a theoretical upper bound for the outflow speed. 4.c) Produce a suitable graph to compare your measurement results with the theoretical upper bound. Assess how well the experimentally determined speeds match the theoretically expected maximum. 4. (d) Name at least two physical reasons that may be responsible for possible deviations between the theoretical prediction and the experimental results. Qualitatively justify how these influence the results. The first is the ‘Junior Problem’ (10 points). Long line High-voltage lines are used to transport electrical energy over long distances. The sketch shows the cross-section of a simple high-voltage line. The inner conductor is a steel cable and the six conductors lying on the outside are made of aluminum. The diameter of each of the individual cables is $d = 1, 5 cm$ and the length of the high-voltage line is denoted by $L$ . The steel cable is important for the mechanical stability but is less well suited for electrical conduction, since the resistivity of steel, $ρ_{St} = 1, 5 \cdot 1 0^{- 7} Ω m$ , is significantly higher than that of aluminum, $ρ_{Al} = 2, 7 \cdot 1 0^{- 8} Ω m$ . Denote by $R$ the resistance of the high-voltage line. If the central steel cable is removed, this resistance increases by $Δ R = 6, 1 \cdot 1 0^{- 4} Ω$ . Determine the length $L$ of the high-voltage line. r n Laser beam d Other, of a kind used for the manufacture of goods Al Al Al Al Al Al d Sketch of the polymer sphere with laser beam. Cross-section sketch of a high-voltage line. 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! Physics at its peak at the PhysicsOlympic The PhysicsOlympic in Germany is for all students who enjoy physics and have a taste for tricky theoretical problems as well as exciting experiments. Apart from the actual competition, there are also great opportunities to deepen knowledge, to meet other people enthusiastic about physics, and to experience science together. The PhysicsOlympiade in Germany is part of the ScienceOlympiades, which are coordinated by the Leibniz Institute for Science and Mathematics Education in Kiel (IPN) in cooperation with the education ministries of the federal states and funded by the BMBFSFJ. For the best five, the competition leads after four rounds to the International Physics Olympiad (IPhO), which is held each year in a different country. The host country for the IPhO 2027 has not yet been determined. The entry with the 1st round In the 1st round of the PhysicsOlympics in Germany, the four problems on this problem sheet are to be solved alone and as homework by the beginning of September 2026. Participants who, after the summer holidays, are not yet in the second-to-last grade level can earn a points bonus with the junior problem. Further information on rules, procedure and deadlines can be found at www.ipho.info. 1st round for the IPhO 2027 the procedure at a glance 1 2 3 4 5 Correction phase Starting on 1 April 2026 September 2026 Teachers The students Start of the first round Reaching out to interested students Register & Sign up Support with material & with questions Looking at the problems and collecting ideas Register & Sign up Correcting based on the model solution Personal code to students Working on the problems of the 1st round Submission of the work Deadline 7 September *) Feedback on results in October Submission to the teacher Entering the results & submitting the work The deadline for the submission of the application 1 2 3 4 5 Registration and working period Aprilbeginning of September 2026 *) Teachers may also arrange other dates at their own discretion, as long as the deadline for reporting results on 25 September 2026 is met. What’s next? Whoever reaches at least 30 points in the first round is invited to the second round, which is written as an exam. After that, with the national and final round, the third and fourth stages of the competition, each as week-long events at a research site in Germany. In every round there are materials for learning and training. In addition, a variety of offerings, such as the Orpheus seminars, provide opportunities to broaden one’s own horizons and to exchange ideas with other people enthusiastic about physics.

Curious? Then join in! We wish all students and supervising teachers much success at the PhysicsOlympic and much fun with the problems! What questions? The team of the PhysicsOlympic at the IPN and the state representatives are happy to help. Contact for the competition management PhysikOlympiade $\cdot$ IPN Olshausen Street. 62 $\cdot$ 24118 Kiel The Commission has also adopted a number of proposals for the implementation of the programme. 0431 880-5120 or -5387 The cover image was taken by the FotoAG of the student research center at the Werner-Heisenberg High School in Heide. International

The Physics Olympiad Contact for the state representatives The addresses of the state representatives, who coordinate the conduct of the first two rounds in the federal states, can be found at www.ipho.info.

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