IPhO 2026

Problem 1 (10 points) Ice-cold research Samples from the depths of the Arctic and Antarctic ice sheets can provide information about the climate in long-past eras. During the drillings in the NEEM project (North Greenland Eemian Ice Drilling), ice-core samples were obtained in Greenland from the central ice sheet at depths of more than 2500 m. The uppermost layers of the Greenland ice sheet consist of so-called firn snow, which is compressed into ice as the depth increases. The graph shown below presents the density in the uppermost part of the Greenland ice sheet as a function of the depth below the surface. Consider a sample from the ice core that has approximately the shape of a cylinder with diameter $d = 9, 8 cm$ and height $h = 2, 0 cm$ . The mass of the sample is $m_{Eis} = 119, 5 g$ . 1.a) Calculate the approximate density of the sample and determine from which depth of the ice sheet it originates. In reality the sample is not perfectly cylindrical, which gives rise to errors in the density determination. An alternative method for determining the density avoids this problem. For this, a beaker is filled with water and placed on a scale. The sample is then added to the beaker so that it floats in the water. Finally, the sample is pushed underwater with a pointed object. The masses displayed by the scale in these three situations are $m_{1} = 726, 3 g$ (beaker with water), $m_{2} = 845, 8 g$ (with the sample added) and $m_{3} = 873, 0 g$ (with the sample pushed down). 1.b) Use this to determine a more accurate value for the density of the sample and the depth at which it was taken. Make no assumption about the shape of the sample and use for the density of water the value $ρ_{Wasser} = 1000 kg m^{- 3}$ . By examining chemical impurities and isotope ratios, the thickness of the annually deposited ice layers in the ice core can be determined. Under pressure, ice exhibits properties of a fluid. Therefore the ice in the Greenland ice cover is not only compressed but also moves toward the coasts away from the ice shelf. This leads to the annually deposited ice layers becoming thinner with increasing depth. The following table gives the thickness of the ice layers in meters per year for the NEEM core:

Depth z in m 0 500 1000 1200 1400 1500 1600 Thickness per year $λ$ in m a $^{- 1}$ 0.25 0.20 0.13 0.10 0.037 0.018 0.010 1.c) Using the data from the table, produce a graph that approximately shows the age t of an ice sample as a function of the depth z at which the sample was taken. 1.d) Use this to determine the ages $t_{1}$ and $t_{2}$ of two ice-core samples taken at depths of $z_{1} = 300 m$ and $z_{2} = 1600 m$ . Studies of the samples allow conclusions to be drawn about climate changes. An important indicator for this is the quantity $δ^{18}$ O, which compares the ratio of the stable oxygen isotopes $^{18}$ O to $^{16}$ O in the ice with a reference value. Studies of the Greenland ice layer show that there is an approximately linear relationship between this quantity and the temperature above the ice layer, as can be seen in the figure at the top right. For the two examined samples the $δ^{18}$ O values are $δ_{1} = - 34, 5$ ‰ and $δ_{2} = - 43, 2$ ‰. 1.e) Approximately determine the temperatures $T_{1}$ and $T_{2}$ that prevailed above the ice layer at the time each of the two ice samples formed, and calculate the difference between the temperatures. The problems are best hung directly next to the poster! Problems and further materials for download Map of Greenland with the position of the NEEM camp (map by Uwe Dedering, CC BY-SA 3.0). NEEM Relationship between the density of the ice at the NEEM drilling site and the depth. 400 500 600 700 800 900 0 50 100 150 200 250 Density in kg m $^{- 3}$ Depth in m Observed relationship between $δ^{18}$ O in snow and the average annual surface temperature T. $- 60$ $- 40$ $- 20$ 0 20 $- 60$ $- 50$ $- 40$ $- 30$ $- 20$ $- 10$ 0 10 T in $^{\circ}$ C $δ^{18}$ O in ‰

Topic: Fluid Mechanics, Thermodynamics, Conservation of Energy Metodi: Hydrostatic Equilibrium, Calculus-Integration, Graph Linearization Competenze: Graph Linearization, Mathematical Modeling, Experimental Data Analysis Objects: Cylinder, Container Fonte: Testo (PDF) — p.2

Problema 1 (10 punti) Ricerca ice-cold I campioni delle profondità dei ghiacci dell’Artico e dell’Antartide possono fornire informazioni sul clima in epoche del passato. Durante i perforazioni nel progetto NEEM (North Greenland Eemian Ice Drilling), campioni di ghiaccio-core sono stati ottenuti in Groenlandia dal calotto centrale a profondità di oltre 2500 m. I livelli più alti della calotta glaciale del Groenlandia sono composti da neve firn, che viene compressa in ghiaccio man mano che aumenta la profondità. Il grafico mostrato sotto presenta la densità nella parte superiore del ghiaccio della Groenlandia come funzione della profondità sotto la superficie. Considerate un campione del nucleo glaciale che ha circa la forma di un cilindro con diametro $d = 9, 8 cm$ e altezza $h = 2, 0 cm$ . La massa del campione è $m_{Eis} = 119, 5 g$ . 1.a) Calcolare la densità approssimativa del campione e determinare da quale profondità del ghiaccio esso proviene. In realtà il campione non è perfettamente cilindrico, il che dà luogo ad errori nella determinazione della densità. Un metodo alternativo per determinare la densità evita questo problema. Per questo, un bicchiere è riempito di acqua e posto su una scala. Il campione viene poi aggiunto al beaker in modo che galleggi in acqua. Finalmente, il campione è spinto sotto l’acqua con un oggetto puntato. Le masse mostrate dalla scala in queste tre situazioni sono $m_{1} = 726, 3 g$ (beaker with water), $m_{2} = 845, 8 g$ (with the sample added) e $m_{3} = 873, 0 g$ (with the sample pushed down). 1.b) Usare questo per determinare un valore più accurato per la densità del campione e la profondità a cui è stato preso. Non fare presupposto sulla forma del campione e utilizzare per la densità di acqua il valore $ρ_{Wasser} = 1000 kg m^{- 3}$ . Esaminando le impurità chimiche e i rapporti isotopici, si può determinare lo spessore dei ghiacci depositati annualmente nel nucleo del ghiaccio. Sotto pressione, il ghiaccio mostra proprietà di un fluido. Pertanto, il ghiaccio della copertura glaciale della Groenlandia non solo si comprime ma si muove verso le coste lontano dalla piattaforma glaciale. Ciò porta ai livelli di ghiaccio depositati annualmente a diventare più sottili con una profondità crescente. La tabella seguente dà lo spessore dei livelli di ghiaccio in metri per anno per il nucleo NEEM:

Profondità z in m 0 500 1000 1200 1400 1500 1600 Spessore per anno $λ$ in m a $^{- 1}$ 0.25 0.20 0.13 0.10 0.037 0.018 0.010 1.c) Usando i dati della tabella, produrre un grafico che mostra approssimativamente l’età t di un campione di ghiaccio come funzione della profondità z a cui è stato preso il campione. 1.d) Use this to determine the ages $t_{1}$ and $t_{2}$ of two ice-core samples taken at depths of $z_{1} = 300 m$ and $z_{2} = 1600 m$ . Studi dei campioni consentono di trarre conclusioni sui cambiamenti climatici. Un importante indicatore per questo è la quantità $δ^{18}$ O, che confronta il rapporto degli isotopi di ossigeno stabile $^{18}$ O a $^{16}$ O nel ghiaccio con un valore di riferimento. Studi sul livello di ghiaccio della Groenlandia mostrano che c’è una relazione lineare approssimativa tra questa quantità e la temperatura sopra il livello di ghiaccio, come si può vedere nella figura in alto a destra. Per i due campioni esaminati i valori di $δ^{18}$ O sono $δ_{1} = - 34, 5$ ‰ e $δ_{2} = - 43, 2$ ‰. 1.e) Approximately determinare le temperature $T_{1}$ e $T_{2}$ che prevalevano sopra il livello di ghiaccio al momento in cui ciascuno dei due campioni di ghiaccio si formò, e calcolare la differenza tra le temperature. I problemi sono meglio affamato direttamente vicino a Il poster! Problemi e altri materiali per download Map of Greenland with the position of the NEEM camp (map by Uwe Dedering, CC BY-SA 3.0). No Relazione tra la densità del ghiaccio nel sito di perforazione NEEM e la profondità. 400 500 600 700 800 900 0 50 100 150 200 250 Densità in kg m $^{- 3}$ profondità in m Relazione osservata tra $δ^{18}$ O in snow and the average annual surface temperature T. $- 60$ $- 40$ $- 20$ 0 20 $- 60$ $- 50$ $- 40$ $- 30$ $- 20$ $- 10$ 0 10 T in $^{\circ}$ C $δ^{18}$ O in ‰

The following points are added: Ice-cold research Samples from the depths of the Arctic and Antarctic ice sheets can provide information about the climate in long-past eras. During the drilling in the NEEM project, ice core samples were obtained in Greenland from the central ice sheet at depths of more than 2500 m. The uppermost layers of the Greenland ice sheet consist of so-called firn snow, which is compressed into ice as the depth increases. The graph shown below presents the density in the uppermost part of the Greenland ice sheet as a function of the depth below the surface. Consider a sample from the ice core that has approximately the shape of a cylinder with diameter $d = 9, 8 cm$ and height $h = 2, 0 cm$ . The mass of the sample is $m_{Eis} = 119, 5 g$ .

(a) Calculate the approximate density of the sample and determine from which depth of the ice sheet it originates. In reality the sample is not perfectly cylindrical, which gives rise to errors in the density determination. An alternative method for determining the density avoids this problem. For this, a beaker is filled with water and placed on a scale. The sample is then added to the beaker so that it floats in the water. Finally, the sample is pushed underwater with a pointed object. The masses displayed by the scale in these three situations are $m_{1} = 726, 3 g$ (beaker with water), $m_{2} = 845, 8 g$ (with the sample added) and $m_{3} = 873, 0 g$ (with the sample pushed down).
(b) Use this to determine a more accurate value for the density of the sample and the depth at which it was taken. Make no assumption about the shape of the sample and use for the density of water the value $ρ_{Wasser} = 1000 kg m^{- 3}$ . By examining chemical impurities and isotope ratios, the thickness of the annually deposited ice layers in the ice core can be determined. Under pressure, ice exhibits properties of a fluid. Therefore, the ice in the Greenland ice cover is not only compressed but also moves towards the coasts away from the ice shelf. This leads to the annually deposited ice layers becoming thinner with increasing depth. The following table gives the thickness of the ice layers in meters per year for the NEEM core:

Depth z in m 0 500 1000 1200 1400 1500 1600 Thickness by weight year $λ$ in m a $^{- 1}$ 0.25 0.20 0.13 0.10 0.037 0.018 0.010 1.c) Using the data from the table, produce a graph that approximately shows the age t of an ice sample as a function of the depth z at which the sample was taken. 1.d) Use this to determine the ages $t_{1}$ and $t_{2}$ of two ice-core samples taken at depths of $z_{1} = 300 m$ and $z_{2} = 1600 m$ . Studies of the samples allow conclusions to be drawn about climate change. An important indicator for this is the quantity $δ^{18}$ O, which compares the ratio of the stable oxygen isotopes $^{18}$ O to $^{16}$ O in the ice with a reference value. Studies of the Greenland ice layer show that there is an approximately linear relationship between this quantity and the temperature above the ice layer, as can be seen in the figure at the top right. For the two samples examined the $δ^{18}$ O values are $δ_{1} = - 34, 5$ ‰ and $δ_{2} = - 43, 2$ ‰. 1.e) Approximately determine the temperatures $T_{1}$ and $T_{2}$ that prevailed above the ice layer at the time each of the two ice samples formed, and calculate the difference between the temperatures. The problems Are best hung directly next to The poster! Problems and further materials for download Map of Greenland with the position of the NEEM camp (map by Uwe Dedering, CC BY-SA 3.0). No Relationship between the density of the ice at the NEEM drilling site and the depth. 400 500 600 700 800 900 0 50 100 150 200 250 Density in kg m $^{- 3}$ Depth in m Observed relationship between $δ^{18}$ O in snow and the average annual surface temperature T. $- 60$ $- 40$ $- 20$ 0 20 $- 60$ $- 50$ $- 40$ $- 30$ $- 20$ $- 10$ 0 10 T in $^{\circ}$ C $δ^{18}$ O in ‰

Problem 2 (10 points) Strongly accelerated Determine the magnitudes of the accelerations $a_{1}$ to $a_{4}$ and express them as a multiple of the gravitational acceleration $g = 9, 81 ms^{- 2}$ at the Earth’s surface. $a_{1}$ The acceleration of a tennis ball with a mass of 57.0 g that, during a serve, is uniformly accelerated over a distance of 40 cm to a speed of 150 km h $^{- 1}$ . $a_{2}$ The acceleration of a wet sock in a washing-machine drum with a diameter of 50 cm during the spin cycle at 1400 revolutions per minute. $a_{3}$ The acceleration experienced by an electron between the plates of a capacitor that are 10 cm apart, across whose plates a voltage of 1.0 V is applied. $a_{4}$ The gravitational acceleration caused by the Sun at $1, 0 \cdot 1 0^{5}$ km above the photosphere.

Topic: Newtonian Mechanics, Electrostatics, Gravitation Metodi: Kinematic Equations, Lorentz Force Analysis, Newton’s Law of Gravitation Competenze: Unit Conversion, Physical Reasoning, Estimation & Approximation Objects: Ball, Electron, Capacitor, Star Fonte: Testo (PDF) — p.3

Problema 2 (10 punti) Strongly accelerated Determina le magnitudini delle accelerazioni $a_{1}$ a $a_{4}$ e esprimile come un multiple dell’accelerazione gravitazionale $g = 9, 81 ms^{- 2}$ alla superficie della Terra. $a_{1}$ L’accelerazione di una palla da tennis con una massa di 57,0 g che, durante un servizio, è uniformemente accelerata su una distanza di 40 cm a una velocità di 150 km h $^{- 1}$ . $a_{2}$ L’accelerazione di una calzatura bagnata in un batteria di lavanderia con un diametro di 50 cm durante il ciclo di spin a 1400 rivoluzioni al minuto. $a_{3}$ L’accelerazione vissuta da un elettrone tra le piastre di un condensatore che sono 10 cm separati, attraverso le cui piastre è applicata una voltage di 1,0 V. $a_{4}$ The gravitational acceleration caused by the Sun at $1, 0 \cdot 1 0^{5}$ km above the photosphere.

Problem 3 (10 points) Well charged In a box in the physics collection you find a battery with voltage $U$ , cables, and two identical capacitors of capacitance $C$ . Find a way to reach as high a voltage as possible with these components. Describe how you have to proceed to do so and determine the value of the voltage achievable in this way. Hint: It is possible to reach voltage values greater than $3 U$ .

Topic: Circuits, Electrostatics Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction, Energy Conservation Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Battery, Capacitor, Wire Fonte: Testo (PDF) — p.3

Problema 3 (10 punti) Bene caricato In a box in the physics collection you find a battery with voltage $U$ , cables, and two identical capacitors of capacitance $C$ . Trova un modo per raggiungere la massima tensione possibile con questi componenti. Descrivere come devi procedere a farlo e determinare il valore della tensione raggiungibile in questo modo. Insegna: è possibile raggiungere valori di tensione superiori a $3 U$ .

Problem 4 (10 points) Flown high Not all the way to the Moon, but at least a good stretch up to the ceiling, can a ballpoint-pen refill fly. To do this, unscrew a ballpoint pen with a large-capacity refill and press the refill as far as possible against the spring into the pen. When you then release the refill, it shoots out of the unscrewed pen. Depending on the design of the pen, it can be useful to place the spring in the upper part of the pen and, if necessary, fix it with a bit of tape so that it does not fly off as well. 4.a) Use a ruler to measure the distance by which the spring is compressed before launch. 4.b) Using a suitable measurement method, determine the maximum rise height of the refill during its flight. 4.c) Using your measured values, determine the speed of the refill at launch. 4.d) Measure the mass of the ruler with a scale. Using only the ruler and the pen, determine the mass of the refill. 4.e) Calculate the spring constant of the spring in the pen and the maximum “thrust” on the refill. Junior problem (10 points) Driving safely A rule of thumb for the safe following distance in road traffic is “distance in meters equals half the speedometer value.” Here it is assumed that the speedometer value is displayed in kilometers per hour. Consider a single-lane country road heavily traveled by cars, on which all drivers follow this rule. 5.a) Estimate how many cars can at most pass a given point of the road in one hour. Take into account that a car has a length. If now one of the cars suddenly brakes, the following cars must also reduce their speed. In doing so, drivers often brake their car harder than the vehicle directly ahead. Assume that one car suddenly reduces its speed from $v = 100$ km h $^{- 1}$ by $Δ v = 30$ km h $^{- 1}$ and that each following car brakes in such a way that its change in speed is 20 % greater than the change in speed of the car directly ahead. 5.b) Show that in this way the traffic can come to a complete standstill, and state which car behind the one that braked first is the first to come to a stop. Ballpoint-pen rocket before launch. 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! scienceolympiaden.de Show your talent! Students If you are a student, the IPhO and the PhysikOlympiade in Germany offer you many 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 being there. Successfully completing the first round is already a special achievement and a real distinction. So, just be brave! Teachers As a teacher, you can use the problems of the PhysikOlympiade to offer particularly capable or interested students a challenge in physics and to encourage them toward a deeper engagement with physics topics. The PhysikOlympiade can thus serve as an instrument of individual support. In particular, the problems of the 1st round are suitable not only for the best in a class.

With a wide range of offerings, the PhysikOlympiade aims to reach interested young people broadly and to inspire them lastingly for the natural sciences. To this end, support offerings such as the Orpheus seminars and the accompanying materials for the 1st round serve, with which we want to support you in introducing students to topics of the PhysikOlympiade. So please encourage your students to take part; for only those who do not participate can lose. Schools By encouraging participation in competitions, schools can sharpen their profile and use these, in the sense of enrichment, as a complement to school offerings. Competitions thereby offer 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 especially motivated and high-achieving young people. Nevertheless, participation in the entry rounds too is not only worthwhile 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. By the way, in many federal states participation can be recognized as a special academic achievement or as a subject/seminar paper of your students for the Abitur. Interested in more than physics? The IPhO is one of the six nationwide science student competitions organized by the IPN – the ScienceOlympiaden. In addition to the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO), and Physics (IPhO), these include the International Junior Science Olympiad (IJSO), the European Olympiad of Experimental Science (EOES), and the BundesUmweltWettbewerb (BUW). Together they address students from the beginning of secondary school through to the end of their school years and, with a close network, offer the possibility of lasting support for scientific abilities and interests. Further information at: www.scienceolympiaden.de Many good reasons to take part in the PhysikOlympiade Greetings The Federal Minister of Education and Research and the President of the Conference of Education Ministers invite participation in the ScienceOlympiaden, to which the PhysikOlympiade belongs. © Janine Schmitz, Photothek © Photo: Anne Karsten Dear students, dear parents and teachers, the re-founder of the Olympic Games, Pierre de Coubertin, once said: “The most important thing at the Olympic Games is not to win, but to take part.” This transfers wonderfully to the ScienceOlympiaden. I would even go further: whoever takes part wins in any case. Perhaps not a place on the winners’ podium, but a great experience. Disciplines such as mathematics, computer science, or the natural sciences too thrive not only on the thousandfold practiced, on knowledge and ability. They also thrive on the courage and the joy of entering into competition with others for the best ideas and solutions. Be it the small innovation from one’s own garden or a patent-worthy approach to saving lives. There is so much more in biology, chemistry, and physics than the next school grade. Above all: it is up to us how we further explore the laws of nature, how we use them, and how much energy we now invest in tasks for humanity such as saving the climate or dealing with artificial intelligence. Countless questions can only be answered with STEM knowledge. That is why we need you, dear STEM fans, so urgently. Of course not only the top finishers, but all who are interested in and can be inspired by the subjects of mathematics, computer science, the natural sciences, and technology. Around 10,000 students take part each year in the ScienceOlympiaden and the BundesUmweltWettbewerb. They experience the very special time at the large meetings, the fun of experimenting, thinking, and rethinking. They form

Topic: Newtonian Mechanics, Conservation of Energy, Oscillations & Waves Metodi: Energy Conservation Method, Hooke’s Law, Kinematic Equations Competenze: Measurement & Instrumentation, Mathematical Modeling, Estimation & Approximation Objects: Spring, Projectile Fonte: Testo (PDF) — p.3

Problema 4 (10 punti) Flotta alta Non tutta la strada per la Luna, ma almeno un buon stretch fino al soffitto, può un ballpoint-pen riempire volano. Per fare questo, scrolla una penna ballpoint con un riempimento a grande capacità e premere il riempimento per quanto possibile contro la primavera nella penna. Quando poi rilasci il riempimento, spara fuori dalla penna scrollata. A seconda del design della penna, può essere utile mettere la molla nella parte superiore della penna e, se necessario, fissarla con un po’ di nastro in modo che non vola fuori pure. 4.a) Utilizzare un ruoter per misurare la distanza da cui la spruzzata è compressa prima del lancio. 4.b) Determina l’altezza massima di rallentamento del riempimento durante il suo volo, utilizzando un metodo di misurazione appropriato. 4.c) Usando i valori misurati, determinare la velocità del riempimento al lancio. 4.d) Misurare la massa del ruoter con una scala. Usando solo il ruler e la penna, determinare la massa del riempimento. 4.e) Calcolare la costante di molla della molla e la massima “tresta” sul riempimento. Problema minore (10 punti) Guidare in modo sicuro Una regola fondamentale per la distanza sicura in traffico stradale è “distanza in metri equivale a metà del valore del velocometro”. Qui si presume che il valore del velocometro sia visualizzato in chilometri per ora. Considerate una strada di campagna a singolo tratto pesantemente percorsa da auto, in cui tutti i conducenti seguono questa regola. 5. (a) Estimare quanti auto possono passare al massimo un determinato punto della strada in un’ora. Tieni presente che una macchina ha una lunghezza. Se una delle auto si frena improvvisamente, le seguenti devono ridurre la velocità. In tal modo, i conducenti spesso frenano la loro auto più duramente del veicolo direttamente davanti. Supponiamo che una macchina riduca improvvisamente la sua velocità da $v = 100$ km h $^{- 1}$ da $Δ v = 30$ km h $^{- 1}$ e che ogni successiva macchina freni in modo tale che il suo cambiamento di velocità sia del 20% maggiore del cambiamento di velocità della macchina direttamente avanti. 5.b) Mostrare che in questo modo il traffico può venire a un completo stallo, e affermare quale auto dietro quella che ha frenato prima è il primo a venire a un stop.

Ballpoint-pen rocket before launch. 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! sciencesolymppiaden.de Mostra il tuo talento! Studenti Se sei uno studente, l’IPhO e la PhysicsOlympic in Germania ti offrono molte opportunità per impegnarti intensamente con le domande di fisica, per sperimentare la fisica come una disciplina scientifica eccitante, per testare i tuoi limiti, e non ultimo per incontrare persone interessanti. Per i round di competizione ci sono materiali di apprendimento e problemi di formazione che ti aiutano a approfondire le tue conoscenze e le tue capacità di risoluzione dei problemi. Ai seminari incontrerai molti altri giovani entusiasti di fisica. Quindi, è utile partecipare in ogni caso, indipendentemente dal fatto che tu sia in grado di raggiungere i round superiori. Quello che conta è essere lì. Completare con successo il primo round è già un’impresa speciale e una vera distinzione. Allora, be brave! Docenti Come insegnante, puoi usare i problemi della fisicaOlimpade per offrire a studenti particolarmente capaci o interessati una sfida in fisica e per incoraggiarli verso un impegno più profondo con i temi della fisica. La PhysicsOlympiade può quindi servire come strumento di sostegno individuale. In particolare, i problemi del primo round sono adatti non solo ai migliori di una classe.

Con una vasta gamma di offerte, la PhysicsOlympiade mira a raggiungere i giovani interessati in modo ampio e a ispirarli duratamente per le scienze naturali. Per questo scopo, offerte di supporto come i seminari Orpheus e i materiali che accompagnano il primo round servono, con cui vogliamo supportarti nell’introduzione degli studenti a argomenti della fisicaOlimpiade. Quindi, per favore, incoraggi i tuoi studenti a partecipare, perché solo coloro che non partecipano possono perdere. Scuole Incoraggiando la partecipazione a competizioni, le scuole possono accentuare il loro profilo e utilizzare questi, nel senso di arricchimento, come un complemento alle offerte scolastiche. Le competizioni offrono così ambienti di apprendimento diversificati e differenziati per gli studenti partecipanti. Nel settore delle materie STEM, le Olimpiadi, almeno nei prossimi round, rappresentano una competizione rivolta a giovani particolarmente motivati e di alto livello. Tuttavia, partecipare ai round di entrata non solo vale la pena, ma può anche contribuire a un’entusiasmo duraturo per i temi STEM. Offerte come i seminari Orpheus consentono il supporto di un gran numero di partecipanti. A proposito, in molti stati federali la partecipazione può essere riconosciuta come un’academic achievement speciale o come un tema/seminar paper of your students for the Abitur. Interessato in più della fisica? L’IPhO è uno dei sei concorsi nazionali per studenti di scienza organizzati dall’IPN the ScienceOlympics. In aggiunta alle competizioni di selezione per le Olimpiadi internazionali in Biologia (IBO), Chimica (IChO), e Fisica (IPhO), queste includono l’International Junior Science Olympiad (IJSO), l’European Olympiad of Experimental Science (EOES), e il BundesUmweltWettbewerb (BUW). Insieme si rivolge agli studenti dall’inizio della scuola secondaria fino alla fine dei loro anni scolastici e, con una rete stretta, offre la possibilità di supporto duraturo per abilità e interessi scientifici. Informazioni aggiuntive: www.scienceolympiaden.de Molti buoni motivi per partecipare alla fisicaOlimpico Salve, grazie. Il ministro federale dell’istruzione e della ricerca e il presidente della Conferenza dei ministri dell’istruzione invitano la partecipazione alle ScienceOlympiade, a cui appartiene la PhysicsOlympiade. © Janine Schmitz, Fotothek © Foto: Anne Karsten Cari studenti, Cari genitori e insegnanti, il fondatore degli Olimpiadi, Pierre de Coubertin, una volta disse: “La cosa più importante ai Giochi Olimpici non è vincere, ma prendere parte”. Questo trasferisce meravigliosamente alle ScienceOlympics. Io andrei anche oltre: chi partecipa vince in ogni caso. Forse non un posto sul podio dei vincitori, ma un’esperienza fantastica. Discipline come le matematiche, le informatiche o le scienze naturali prosperano non solo sulla migliaia di volte praticate, ma anche sulla conoscenza e capacità. Si sviluppa anche con il coraggio e la gioia di competere con gli altri per le migliori idee e soluzioni. Che sia la piccola innovazione dal proprio giardino o un approccio degno di brevetto per salvare vite. C’è molto di più in biologia, chimica e fisica che nel corso di scuola. Soprattutto, dipende da noi come esploriamo ulteriormente le leggi della natura, come le usiamo, e quanta energia investiamo ora in attività per l’umanità come salvare il clima o affrontare l’intelligenza artificiale. Numerose domande possono essere risposte solo con la conoscenza STEM. Ecco perché abbiamo bisogno di voi, cari fan di STEM, con tanta urgenza. Naturalmente non solo i migliori, ma tutti coloro che sono interessati e possono essere ispirati dai soggetti di matematica, informatica, scienze naturali e tecnologia. Circa 10.000 studenti partecipano ogni anno al concorso ScienceOlympiaden und der Bundesumwelt. Esperiiscono il momento molto speciale alle grandi riunioni, il divertimento di sperimentare, pensare e ripensare. Si formano

Problem 4 (10 points) Flown high Not all the way to the moon, but at least a good stretch up to the ceiling, can a ballpoint-pen refill fly. To do this, uncrew a ballpoint pen with a large-capacity refill and press the refill as far as possible against the spring into the pen. When you then release the refill, it shoots out of the unscrewed pen. Depending on the design of the pen, it can be useful to place the spring in the upper part of the pen and, if necessary, fix it with a bit of tape so that it doesn’t fly off as well. 4. (a) Use a ruler to measure the distance by which the spring is compressed before launch. 4. (b) Using a suitable measurement method, determine the maximum rise height of the refill during its flight. 4.c) Using your measured values, determine the speed of the refill at launch. 4.d) Measure the mass of the ruler with a scale. Using only the ruler and the pen, determine the mass of the refill. 4. (e) Calculate the spring constant of the spring in the pen and the maximum “thrust” on the refill. The first is the ‘Junior Problem’ (10 points). Driving safely A rule of thumb for the safe following distance in road traffic is “distance in meters equals half the speedometer value”. Here it is assumed that the speedometer value is displayed in kilometers per hour. Consider a single-lane country road heavily traveled by cars, on which all drivers follow this rule. 5. (a) Estimate how many cars can at most pass a given point of the road in one hour. Take into account that a car has a length. If now one of the cars suddenly brakes, the following cars must also reduce their speed. In doing so, drivers often brake their car harder than the vehicle directly ahead. Assume that one car suddenly reduces its speed from $v = 100$ km h $^{- 1}$ by $Δ v = 30$ km h $^{- 1}$ and that each following car brakes in such a way that its change in speed is 20% greater than the change in speed of the car directly ahead. 5.b) Show that in this way the traffic can come to a complete stop, and state which car behind the one that brake first is the first to come to a stop. Ballpoint pen rocket before launch. 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! The European Commission has decided to extend the period of validity of the decision. Show your talent! The students If you are a student, the IPhO and the PhysicsOlympic in Germany offer you many 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 being there. Successfully completing the first round is already a special achievement and a real distinction. So, just be brave! Teachers As a teacher, you can use the problems of the physics Olympiade to offer particularly capable or interested students a challenge in physics and to encourage them towards a deeper engagement with physics topics. The PhysicsOlympiade can thus serve as an instrument of individual support. In particular, the problems of the 1st round are suitable not only for the best in a class.

With a wide range of offerings, the PhysicsOlympiade aims to reach interested young people broadly and to inspire them lastingly for the natural sciences. To this end, support offerings such as the Orpheus seminars and the accompanying materials for the 1st round serve, with which we want to support you in introducing students to topics of the PhysicsOlympic. So please encourage your students to take part; for only those who do not participate can lose. Schools By encouraging participation in competitions, schools can sharpen their profile and use these, in the sense of enrichment, as a complement to school offerings. Competitions thus offer 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 especially motivated and highly achieving young people. Nevertheless, participation in the entry rounds is not only worthwhile 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. By the way, in many federal states participation can be recognized as a special academic achievement or as a subject/seminar paper of your students for the Abitur. Interested in more than physics? The IPhO is one of the six nationwide science student competitions organised by the IPN the ScienceOlympics. In addition to the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO), and Physics (IPhO), these include the International Junior Science Olympiad (IJSO), the European Olympiad of Experimental Science (EOES), and the BundesUmweltwettbewerb (BUW). Together they address students from the beginning of secondary school through to the end of their school years and, with a close network, offer the possibility of lasting support for scientific abilities and interests. 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 PhysicsOlympic Greetings The Federal Minister for Education and Research and the President of the Conference of Education Ministers invite participation in the ScienceOlympics, to which the PhysicsOlympic belongs. The Commission has also adopted a number of measures to combat fraud. © Photo by Anne Karsten Dear students, Dear parents and teachers, The re-founder of the Olympic Games, Pierre de Coubertin, once said, “The most important thing at the Olympic Games is not to win, but to take part”. This transfers wonderfully to the ScienceOlympics. I would even go further: whoever takes part wins in any case. Maybe not a place on the winners’ podium, but a great experience. Disciplines like mathematics, computer science, or the natural sciences too thrive not only on the thousandfold practiced, on knowledge and ability. They also thrive on the courage and joy of competing with others for the best ideas and solutions. Whether it’s the small innovation from one’s own garden or a patent-worthy approach to saving lives. There’s so much more in biology, chemistry, and physics than the next grade. Above all, it’s up to us how we further explore the laws of nature, how we use them, and how much energy we now invest in tasks for humanity like saving the climate or dealing with artificial intelligence. Countless questions can only be answered with STEM knowledge. That’s why we need you, dear STEM fans, so urgently. Of course not only the top finishers, but all who are interested in and can be inspired by the subjects of mathematics, computer science, the natural sciences, and technology. Around 10,000 students take part each year in the ScienceOlympics and the Bundesumweltwettbewerb. They experience the very special time at the big meetings, the fun of experimenting, thinking, and rethinking. They form

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