IPhO 2023

Problem 1 (10 points) Somehow Shifted A thin converging lens forms a sharp image of an object $140, 0 cm$ away on a screen positioned at a distance of $16, 8 cm$ behind the lens. 1.a) Determine the focal length of the lens. Between the lens and the screen, as sketched in the figure, a $3, 0 cm$ thick, plane-parallel glass plate with refractive index $n = 1, 50$ is now placed. To produce a sharp image on the screen again, the screen is shifted by a distance $Δ b$ . 1.b) Explain what effect the glass plate has on a light ray that does not strike it perpendicularly. Use this to justify whether, to produce a sharp image, the screen must be moved closer to the lens or further away from it. 1.c) Determine the magnitude $Δ b$ of the necessary displacement of the screen. You may simplify by assuming that only paraxial rays are involved in the imaging process.

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Snell’s Law, Physical Modeling Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens, Screen Fonte: Testo (PDF) — p.2

Problema 1 (10 punti) In qualche modo spostato Un thin converging lens forma un’immagine acuta di un oggetto $140, 0 cm$ lontano su uno schermo posizionato a una distanza di $16, 8 cm$ dietro il

Il mio corpo è un’arma.

(a) Determina la lunghezza focale del lente. Tra l’obiettivo e lo schermo, come illustrato nella figura, un $3, 0 cm$ spessa, pianta parallela di vetro con indice refraettivo $n = 1, 50$ è ora collocata. Per produrre una schermata acuta di nuovo, la schermata è spostata da una distanza $Δ b$ . 1.b) Spiegare che effetto ha la piastra vetrata su un raggio di luce che non lo colpisce perpendicularmente. Use this to justify whether, to produce a sharp Immagine, lo schermo deve essere spostato più vicino alla lente o più lontano da essa. 1.c) Determina la magnitudo $Δ b$ del necessario dislocazione dello schermo. Potete semplificare assumendo che solo i raggi parazziali sono coinvolti nel processo di immaginazione.

The following points are added: Somehow Shifted A thin converging lens forms a sharp image of an object $140, 0 cm$ away on a screen positioned at a distance of $16, 8 cm$ behind the I’m not going to be able to see it.

(a) Determine the focal length of the lens. Between the lens and the screen, as sketched in the figure, a $3, 0 cm$ thick, plane parallel glass plate with refractive index $n = 1, 50$ is now placed. To produce a sharp image on the screen again, the screen is shifted by a distance $Δ b$ .
(b) Explain what effect the glass plate has on a light ray that does not strike it perpendicularly. Use this to justify whether, to produce a sharp image, the screen must be moved closer to the lens or further away from it. 1.c) Determine the magnitude $Δ b$ of the necessary displacement of the screen. You may simplify by assuming that only paraxial rays are involved in the imaging process.

Problem 2 (10 points) The Tohoku Earthquake Japan lies in a geologically very active region of the Earth, so that earthquakes occur frequently there. On 11 March 2011 at around 14:46 local time the strongest of a whole series of severe earthquakes off the Japanese coast occurred. The hypocentre of this quake lay about $24 km$ below sea level. On the map alongside, four seismic stations in Japan are marked. The table below contains the positions of the measuring stations and the times at which they registered the first signals from the earthquake. Two different times are given, which belong to two different types of waves that are caused by an earthquake and propagate through the Earth’s interior. The so-called P- or primary waves are longitudinal waves. The S- or secondary waves, on the other hand, are transverse waves. The P- and S-waves propagate at different speeds through the Earth’s interior. As a simplification it can be assumed that these speeds are constant and amount, for the P-waves, to $v_{P} = 5, 5 km s^{- 1}$ and, for the S-waves, to $v_{S} = 3, 3 km s^{- 1}$ . Station Position Time of signal registration Abbreviation Name Longitude (N) Latitude (E) P-wave S-wave MIYKNA Miyakonagasawa $3 9^{\circ}$ 34,60′ $14 1^{\circ}$ 49,18′ 14:46:46,71 14:47:9,56 ROKUGO Akitarokugo $3 9^{\circ}$ 23,95′ $14 0^{\circ}$ 37,82′ 14:46:54,18 14:47:23,53 N.KKWH Karakuwa $3 8^{\circ}$ 55,24′ $14 1^{\circ}$ 38,26′ 14:46:40,13 14:46:57,33 N.KAKH Kahoku $3 8^{\circ}$ 30,95′ $14 1^{\circ}$ 20,53′ 14:46:40,57 14:46:57,87 2.a) Using the map, which can also be downloaded as a file at www.ipho.info, and the given data, determine approximately the position of the epicentre of the quake. Also state when the quake occurred. The strength of the earthquake was later given as 9.0 on the so-called moment magnitude scale. Such a strong earthquake is very rare and occurs only every few years. Statistically, one earthquake of magnitude 8 or higher occurs worldwide each year, whereas on average about ten earthquakes of magnitude 7 or higher and 100 with a magnitude of at least 6 are registered each year. The dimensionless moment magnitude scale allows, provided the earthquakes occur under the same conditions, a comparison of the energies $E_{1}$ and $E_{2}$ released by two earthquakes of magnitudes or strengths $M_{1}$ and $M_{2}$ . The following holds: $\frac{E _{1}}{E _{2}} \approx 1 0^{\frac{3}{2} (M_{1} - M_{2})}$ The Tohoku earthquake released more energy than all earthquakes with magnitudes from 6 to 8 together that occur on average worldwide in one year. 2.b) Determine approximately the ratio of these two energies. To do this, simplify by assuming that only earthquakes with integer magnitude occur. Map of Japan in the region around Sendai with measuring stations. Best to hang the problems directly next to the poster! ● ● ● ● MIYKNA ROKUGO N.KKWH N.KAKH ● ● SENDAI FUKUSHIMA 0 50 100km 38 39 40 41 140 141 142 143 eastern longitude northern latitude ? $3, 0 cm$ $140, 0 cm$ Screen Glass plate Lens Object Problems and further materials for download

Topic: Oscillations & Waves, Order-of-Magnitude Estimation Metodi: Kinematic Equations, Order-of-Magnitude Estimation, Approximation & Series Expansion Competenze: Estimation & Approximation, Mathematical Modeling, Experimental Data Analysis Objects: — Fonte: Testo (PDF) — p.2

Problema 2 (10 punti) Il terremoto di Tohoku Il Giappone si trova in una regione geologicamente molto attiva della Terra, quindi i terremoti si verificano spesso lì. On 11 marzo 2011 at around 14:46 local time Il più forte di una serie di terremoti gravi al largo della costa giapponese si è verificato. Il hypocentre of this quake lay about $24 km$ below sea level. Sul mappa, quattro stazioni sismiche in Giappone sono segnate. La tabella seguente contiene le posizioni delle stazioni di misurazione e i tempi in cui hanno registrato i primi segnali dal

Si’, il terremoto. Due diversi tempi sono dati, che appartengono a due diversi tipi di onde che sono causate da un terremoto e si propagano attraverso l’interno della Terra. Il cosiddetto Le onde P o primarie sono onde longitudinali. Le onde S o secondarie, d’altra parte, sono onde transversali. Le onde P e S si propagano a velocità diverse attraverso l’interno della Terra. Come semplificazione si può supporre che queste velocità sono costanti e quantità, per il P-waves, to $v_{P} = 5, 5 km s^{- 1}$ and, for the S-waves, to $v_{S} = 3, 3 km s^{- 1}$ . Stazione Posizione Tempo di registrazione del segnale Abbreviamento Nome Longitudine (N) Latitudine (E) P-wave S-wave Ieri Miyakonagasawa $3 9^{\circ}$ 34,60′ $14 1^{\circ}$ 49,18′ 14:46:46,71 14:47:9,56 ROKUGO Aquacoltura $3 9^{\circ}$ 23,95′ $14 0^{\circ}$ 37,82′ 14:46:54,18 14:47:23,53 N.KKWH Carracova $3 8^{\circ}$ 55,24′ $14 1^{\circ}$ 38,26′ 14:46:40,13 14:46:57,33 N.KAKH Kahoku $3 8^{\circ}$ 30,95′ $14 1^{\circ}$ 20,53′ 14:46:40,57 14:46:57,87 2.a) Using the map, che può essere scaricato come file al sito www.ipho.info, e i dati forniti, determinano approssimativamente la posizione dell’epicentro del terremoto. Quindi, segna quando è avvenuto l’impatto. La forza del terremoto fu poi data come 9.0 sulla cosiddetta scala di magnitudo del momento. Un terremoto così forte è molto forte Rare e si verifica solo ogni pochi anni. Statisticamente, ogni anno si verifica un terremoto di magnitudo 8 o superiore in tutto il mondo, mentre in media si verifica una forte presenza di una fortezza di 3,4 metri. Ogni anno si registrano circa dieci terremoti di magnitudo 7 o superiore e 100 di magnitudo almeno 6. La scala di magnitudo del momento dimensionless permette, a condizione che i terremoti si verificino nelle stesse condizioni, un confronto delle energie $E_{1}$ e $E_{2}$ rilasciate da due terremoti di magnitudini o di potenze $M_{1}$ e $M_{2}$ . Il seguente vale: $\frac{E _{1}}{E _{2}} \approx 1 0^{\frac{3}{2} (M_{1} - M_{2})}$ Il terremoto di Tohoku ha rilasciato più energia di tutti gli altri terremoti con magnitudini da 6 a 8 insieme che si verificano in media in tutto il mondo in un solo giorno
Il mio anno. 2.b) Determina approssimativamente il rapporto di queste due energie. Per fare questo, semplificare assumendo che solo terremoti di magnitudo interi
il numero di persone che hanno ricevuto il trattamento Mappa del Giappone nella regione intorno a Sendai con stazioni di misurazione. Best to hang i problemi direttamente vicino a Il poster! ● ● ● ● Ieri ROKUGO N.KKWH N.KAKH ● ● SONDAI FUKUSHIMA 0 50 100km 38 39 40 41 140 141 142 143 longitudine orientale latitudine settentrionale ? $3, 0 cm$ $140, 0 cm$ Scatto Dischi di vetro Lenti Object Problemi e altri materiali per download

Problem 2 (10 points) The Tohoku earthquake Japan is located in a geologically very active region of the Earth, so earthquakes occur frequently there. On 11 March 2011 at around 14:46 local time The strongest of a whole series of severe earthquakes off the Japanese coast occurred. The hypocentre of this quake lay about $24 km$ below sea level. On the map alongside, four seismic stations in Japan are marked. The table below The first signals from the measuring stations are recorded at the time of the first signals. It’s an earthquake. Two different times are given, which belong to two different types of waves They’re caused by an earthquake and spread through the Earth’s interior. The so-called P- or primary waves are longitudinal waves. The S- or secondary waves, on the other hand, are transverse waves. The P- and S-waves propagate at different speeds through the Earth’s interior. As a simplification it can be assumed that these speeds are constant and amount, for the P-waves, to $v_{P} = 5, 5 km s^{- 1}$ and, for the S-waves, to $v_{S} = 3, 3 km s^{- 1}$ . Station Position of the Time of signal registration Abbreviation of the name Name of the person The following is the list of the following: Latitude (E) P-wave S-wave Other Other articles of heading No. $3 9^{\circ}$ 34,60′ $14 1^{\circ}$ 49,18′ 14:46:46,71 14:47:9,56 Other articles Other articles of heading No. $3 9^{\circ}$ 23,95′ $14 0^{\circ}$ 37,82′ 14:46:54,18 14:47:23,53 N.KKWH Karakuwa $3 8^{\circ}$ 55,24′ $14 1^{\circ}$ 38,26′ 14:46:40,13 14:46:57,33 N.KAKH The following is the list of the countries of the European Union: $3 8^{\circ}$ 30,95′ $14 1^{\circ}$ 20,53′ 14:46:40,57 14:46:57,87 2.a) Using the map, which can also be downloaded as a file at www.ipho.info, and the given data, determine approximately the position of the epicenter of the quake. So state when the quake occurred. The strength of the earthquake was later given as 9.0 on the so-called moment magnitude scale. Such a strong earthquake is very It’s rare and occurs only every few years. Statistically, one earthquake of magnitude 8 or higher occurs worldwide each year, while on average About ten earthquakes of magnitude 7 or higher and 100 with a magnitude of at least 6 are recorded each year. The dimensionless moment magnitude scale allows, provided the earthquakes occur under the same conditions, a comparison of the energies $E_{1}$ and $E_{2}$ released by two earthquakes of magnitude or strength $M_{1}$ and $M_{2}$ . The following holds: $\frac{E _{1}}{E _{2}} \approx 1 0^{\frac{3}{2} (M_{1} - M_{2})}$ The Tohoku earthquake released more energy than all earthquakes with magnitudes from 6 to 8 together that occur on average worldwide in one year. 2. (b) Determine approximately the ratio of these two energies. To do this, simplify by assuming that only earthquakes with integer magnitude occur. Map of Japan in the region around Sendai with measuring stations. Best to hang The problems directly next to The poster! ● ● ● ● Other Other articles N.KKWH N.KAKH ● ● SUNDAY FUKUSHIMA 0 50 100km 38 39 40 41 140 141 142 143 eastern longitude northern latitude ? $3, 0 cm$ $140, 0 cm$ Screen Glass plate Lens The object Problems and further materials for download

Problem 3 (10 points) Flying Racket After losing a match, a player throws his badminton racket away in a high arc. The graph shows the resulting observable motion of the points P and Q marked in the figure alongside. The data points marked in the graph are snapshots at time intervals of $50 ms$ each, beginning at the throw at $x = 0$ . You may assume that the motion of the racket takes place entirely in the $x$ - $y$ plane of the graph. 3.a) Reconstruct the path of the centre of mass S of the racket and draw it into the graph as well. Determine the distances of the points P and Q from the centre of mass. 3.b) Determine the throw speed of the racket both in the horizontal and in the vertical direction as well as the frequency with which the racket rotates in flight. For the analysis you can also download the data points as a table at www.ipho.info and work with them. For the acceleration due to gravity you may use the value $g = 9, 81 m s^{- 2}$ and additionally neglect frictional effects.

Topic: Newtonian Mechanics, Rotational Dynamics Metodi: Kinematic Equations, Free-Body Diagram, Experimental Data Analysis Competenze: Experimental Data Analysis, Graph Linearization, Mathematical Modeling Objects: Projectile Fonte: Testo (PDF) — p.3

Problema 3 (10 punti) Racket volante Dopo aver perso una partita, un giocatore lancia la sua racket di badminton in un arco alto. Il grafico mostra il risultante movimento osservabile dei punti P e Q segnato nella figura accanto. I dati segnati nel grafico sono snapshots a intervalli di tempo di $50 ms$ ciascuno, iniziando al lancio a $x = 0$ . You may assume that the motion of the racket takes place entirely in the $x$ - $y$ plane of the

Graph. 3.a) Riconquistare il percorso del centro di massa S della racket e lo trattiene anche sul grafico. Determina le distanze dei punti P e Q dal centro di massa. 3.b) Determina la velocità di lancio della racket La direzione orizzontale e verticale e la direzione Frequenza con cui il razzo ruota in volo. Per l’analisi è possibile scaricare i data points as a table www.ipho.info e lavorare con loro. Per the acceleration due to gravity you may use the value $g = 9, 81 m s^{- 2}$ e inoltre negliggono gli effetti frattori.

Problem 3 (10 points) Flying racket After losing a match, a player throws his badminton racket away in a high arc. The graph shows the resulting observable motion of the points P and Q marked in the figure next to. The data points marked in the graph are snapshots at time intervals of $50 ms$ each, beginning at the throw at $x = 0$ . You may assume that the motion of the racket takes place entirely in the $x$ - $y$ plane of the I’m going to get a graph. 3.a) Reconstruct the path of the centre of mass S of the racket And draw it into the graph as well. Determine the distances of the points P and Q from the centre of mass. 3.b) Determine the throw speed of the racket both The Commission will take the necessary steps to ensure that the frequency with which the racket rotates in flight. For the analysis you can also download the data points as a table at www.ipho.info and work with them. For the acceleration due to gravity you may use the value $g = 9, 81 m s^{- 2}$ and additionally neglect frictional effects.

Problem 4 (10 points) A Question of Temperature Tea is an integral part of Japanese culture. An important role in the preparation of tea is played by the temperature of the water used. In this problem you are to investigate the cooling of water experimentally, in order to estimate how long one should let boiling water cool before preparing a green tea. For the experiment you need a teapot or alternatively a large mug, hot water, a thermometer, and a clock for measuring time. The thermometer should measure temperatures up to about $50^{\circ} C$ and be able to be immersed in the water. 4.a) Fill about $50^{\circ} C$ hot water into the teapot or the mug. Record the temperature of the water in the vessel as a function of time. You may restrict yourself to a temperature range from $45^{\circ} C$ to about $5^{\circ} C$ above room temperature. Do not forget to stir the water regularly during the experiment. If the temperature of a body does not deviate too strongly from the ambient temperature, Newton’s law of cooling holds to a good approximation. According to it, the power with which heat is given off to the surroundings is approximately proportional to the temperature difference between the body and the surroundings. What exactly “does not deviate too strongly” means depends in the concrete case, among other things, on how accurate the approximation is to be. From the cooling law, for constant ambient conditions, the relation $ϑ (t) = ϑ_{U} + (ϑ_{0} - ϑ_{U}) \cdot e^{- t / τ}$ can be derived* for the evolution of the temperature $ϑ$ of the body. Here $t$ denotes the time, $τ$ the time constant of the cooling, $ϑ_{U}$ the ambient temperature assumed to be constant, and $ϑ_{0}$ the temperature of the body at time $t = 0$ . 4.b) Show that your measured values approximately satisfy the above relation and determine the time constant $τ$ of the cooling in your experiment. 4.c) Using the time constant, estimate roughly how long it takes for boiling water to cool to a temperature of $70^{\circ} C$ for the preparation of green tea in your pot or your mug. Justify why your result is to be expected not to be very accurate and the water actually cools faster. *The derivation is not required here — but feel free to try it out. Junior problem (10 points) Everything in Balance For a mobile, five wind chimes are hung up as shown in the figure. The total mass of all the chimes together is $1, 00 kg$ . The masses of the rods and threads of the mobile can be neglected. Determine what masses $m_{1}$ to $m_{5}$ the individual chimes must have so that the mobile is in equilibrium. P S Q $m_{1}$ $m_{2}$ $m_{3}$ $m_{4}$ $m_{5}$ 10cm 1 2 3 4 5 6 7 1 2 3 x / m y / m g Badminton racket with point markings. The position of the centre of mass S on PQ is unknown. Japanese teapot. To-scale sketch of the mobile. Graph of the trajectories of the points P (●) and Q (x) during the flight. 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 PhysicsOlympiad 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 get to know interesting people. For the competition rounds there are learning materials and training problems that help you to deepen your knowledge and problem-solving skills. At the seminars you meet many other students enthusiastic about physics. Taking part is therefore worthwhile in any case and regardless of whether you make it into the higher rounds. What matters is taking part. Successfully completing the first round is already a special achievement and a genuine distinction. So, just be brave! Teachers As a teacher, with the problems of the PhysicsOlympiad you can offer a challenge to students who are particularly capable or interested in physics and encourage them to engage more deeply with physics topics. In this way the PhysicsOlympiad can 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 its varied offerings, the PhysicsOlympiad aims to appeal broadly to interested young people and to inspire them lastingly for the natural sciences. This is served by 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 feel free to encourage your students to take part; for only those who do not take part can lose. Schools Schools can sharpen their profile by encouraging participation in competitions and use them in the sense of an enrichment as a complement to school offerings. Competitions provide varied, 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-achieving young people. Nevertheless, taking part also 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. In many federal states, by the way, participation can be recognised as a special learning achievement or specialist/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. Besides the selection competitions for the international Olympiads in Biology (IBO), Chemistry (IChO) and Physics (IPhO), these include the International JuniorScienceOlympiad (IJSO), the European ScienceOlympiad (EOES) as well as the Federal Environment Competition (BUW). Together they address students from the beginning of secondary school until after the end of their school years and, with 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 Dear students, dear parents, dear teachers, how does an effective vaccine come about? How do we produce green hydrogen? How do images of brooding icefish come about and what follows from the discovery? The questions that female and male scientists and researchers are concerned with today shape our lives of tomorrow. That is why it is important to understand how the many clever people in science and research work, how they arrive at the right questions and ideas, and how they put their findings into practice. With the competitions organised by the Leibniz Institute for Science and Mathematics Education, we invite you to a voyage of discovery into the realm of science. More than 10,000 students from all over the country embark on this adventure each year and register for the Science- Olympiads and the Federal Environment Competition. Dear students, this is your chance. Join in. Solve exciting problems from biology, chemistry and physics, or work on your own questions about the environment and sustainable development. Use your alert mind, give your creativity room, and inspire yourself and others. For just as important as a clever head is the ability to work well togethe

Topic: Thermodynamics Metodi: Differential Equations, Graph Linearization, Experimental Data Analysis Competenze: Experimental Data Analysis, Graph Linearization, Estimation & Approximation Objects: Container Fonte: Testo (PDF) — p.3

Problema 4 (10 punti) A Question of Temperature Il tè è parte integrante della cultura giapponese. Un ruolo importante nella preparazione del tè è giocato dalla temperatura dell’acqua usata. In questo problema si deve indagare sul raffreddamento dell’acqua sperimentalmente, Per stimare quanto tempo si dovrebbe lasciare che l’acqua bollente si raffreddi prima di preparare un tè verde. Per l’esperimento, hai bisogno di una vasca da tè o, in alternativa, di un grande mug, acqua calda, un termometro e un orologio per misurare il tempo. Il termometro dovrebbe misurare temperature fino a circa $50^{\circ} C$ e essere in grado di essere immersi nell’acqua. 4.a) Riempire $50^{\circ} C$ acqua calda nella teapot o nella tazza. Record the temperature of the water in il veicolo in funzione del tempo. You may restrict yourself to a temperature range from $45^{\circ} C$ a circa $5^{\circ} C$ above room temperature. Non dimenticare di mescolare regolarmente l’acqua durante l’esperimento. Se la temperatura di un corpo non deviano troppo fortemente dalla temperatura ambientale, la legge di Newton del raffreddamento si mantiene ad una buona Approximation. Secondo lui, la potenza con cui il calore viene rilasciato all’ambiente circostante è approssimativamente proporzionale alla differenza di temperatura tra il corpo e l’ambiente circostante. Cosa significa esattamente “non deviare troppo fortemente” dipende dal concreto Casi, tra le altre cose, su quanto accurata sia l’approssimazione. Dal principio di raffreddamento, per le condizioni ambientali costanti, la relazione $ϑ (t) = ϑ_{U} + (ϑ_{0} - ϑ_{U}) \cdot e^{- t / τ}$ can be derived* for the evolution of the temperature $ϑ$ of the body. Qui $t$ denota il tempo, $τ$ la costante di tempo del raffreddamento, $ϑ_{U}$ la temperatura ambientale presunta di essere costante, e $ϑ_{0}$ il temperatura del corpo a tempo $t = 0$ . 4.b) Mostra che i tuoi valori misurati soddisfano circa la relazione sopra e determina la costante di tempo $τ$ del raffreddamento nel tuo

Esperienza. 4.c) Usando il time constant, estimate roughly how long it takes for boiling water to cool to a temperature of $70^{\circ} C$ for the preparation of green tea in your pot or your mug. Justify why your result is to be expected non essere molto accurate e L’acqua effettivamente raffreddata più velocemente. *The derivation is not required here — but feel free to try it out. Problema minore (10 punti) Tutto in equilibrio Per un cellulare, cinque chimes del vento sono appesi come mostrato nella figura. Il La massa totale di tutti i chimes insieme è $1, 00 kg$ . Le masse dei bastoni e dei fili del il mobile può essere trascurato. Determine what masses $m_{1}$ to $m_{5}$ the individual chimes must have in modo che il mobile is in
Equilibrio. P S Q $m_{1}$ $m_{2}$ $m_{3}$ $m_{4}$ $m_{5}$ 10cm 1 2 3 4 5 6 7 1 2 3 x / m y / m g Racket di badminton con punti. La posizione del centro di massa S su PQ è
Non lo so.
Un teapot giapponese. Sketch a scala del cellulare. Grafico delle trajectorie dei punti P (●) e Q (x) durante il periodo di riferimento Il volo. 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 l’Olimpiade di Fisica in La Germania offre molte opportunità a impegnarsi intensamente con le domande di fisica, a sperimentare la fisica Come una disciplina scientifica eccitante, per testare i tuoi limiti e non ultimo per conoscere 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 studenti entusiasti di fisica. In ogni caso, è quindi utile prendere parte. e indipendentemente dal fatto che tu lo faccia in
Rondate superiori. Ciò che importa è
partecipare. Completare con successo Il primo round è già un risultato speciale e una vera distinzione. Allora, be brave! Docenti Come insegnante, con i problemi della PhysicsOlympiad puoi offrire una sfida a studenti particolarmente capaci o interessati alla fisica e incoraggiarli a impegnarsi più profondamente con argomenti di fisica. In questo modo la PhysicsOlympiad può Serve come strumento di sostegno individuale. In particolare, i problemi del 1° Le reti di trasporto a rotonde sono adatte non solo per il
Il migliore di una classe.

Con le sue offerte variate, il PhysicsOlympiad mira ad attrarre ampiamente i giovani interessati e di ispirarli duratamente per il Scienze naturali. Questo è servito da 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 sentitevi liberi di incoraggiare i vostri studenti per il Solo chi non partecipa può perdere. Scuole Le scuole possono aumentare il loro profilo incoraggiando Partecipazione a competizioni e usali nel senso di un arricchimento 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 di alto livello. Tuttavia, partecipare Quindi in entrata round non è solo La Commissione ha adottato una decisione che non è stata adottata. L’entusiasmo per i temi STEM è duraturo. Offerte come le Orpheus seminari consentono il supporto di un Numero di partecipanti. In molti stati federali, comunque, la partecipazione può essere riconosciuta come un’impresa speciale di apprendimento o Paper di seminario/specialista dei vostri studenti per l’abitur. Interessato a più
che la fisica? L’IPhO è uno dei sei concorsi scientifici di studenti nazionali organizzati dall’IPN il Scienza olimpiadi. Oltre alla selezione Competitions for the International Olimpiadi in biologia (IBO), chimica (IChO) e fisica (IPhO), questi includono La Commissione ha inoltre adottato una proposta di regolamento (CE) n. Concorso federale per l’ambiente (BUW). Insieme si indirizzano studenti dall’inizio di scuola secondaria fino a dopo la fine di anni scolastici e, con La rete, offrono la possibilità di sostenere duratamente le capacità e gli interessi scientifici. Informazioni aggiuntive: www.scienceolympiaden.de Molti buoni motivi per partecipare al PhysicsOlympiad Cari studenti, Cari genitori, cari insegnanti, come viene a essere un vaccino efficace? Come produciamo il verde
L’idrogeno? Come vengono le immagini di pesci ghiacciati in panchina E cosa segue dalla scoperta? Le domande che i ricercatori e gli scienziati femminili e maschi sono preoccupati per il fatto che oggi forma le nostre vite di domani. Ecco perché è importante capire come i molti intelligenti Le persone che lavorano in scienza e ricerca le domande e le idee giuste, e come mettono i loro risultati La pratica. Con le competizioni organizzate dall’Istituto Leibniz per la scienza e la tecnologia Matematica Education, vi invitiamo per un viaggio di scoperta nel regno della scienza. Più di 10.000 studenti provenienti da tutto il paese imbarcarsi “On this adventure every year and register for the Science and Technology” (Scienza e tecnologia) Olimpiadi e il concorso federale per l’ambiente. Cari studenti, Questa è la tua occasione. - Si unisca. Solvere problemi eccitanti da biologia, chimica e fisica, o lavorare sulle proprie domande La Commissione ha adottato una proposta di risoluzione sullo sviluppo sostenibile. Usare il tuo allarme mente, dare la tua creatività, e ispirarti e altri. Per quanto importante sia un’intelligenza, è l’abilità di Work well togethe

Problem 4 (10 points) A Question of Temperature Tea is an integral part of Japanese culture. The temperature plays an important role in the preparation of tea of the water used. In this problem you are to investigate the cooling of water experimentally, In order to estimate how long one should let boiling water cool before preparing a green tea. For the experiment you need a teapot or alternatively a large mug, hot water, a thermometer, and a clock for measuring time. The thermometer should measure temperatures up to about $50^{\circ} C$ and be able to be immersed in the water. 4.a) Fill about $50^{\circ} C$ hot water into the teapot or the mug. Record the temperature of the water in The vessel as a function of time. You may restrict yourself to a temperature range from $45^{\circ} C$ to about $5^{\circ} C$ above room temperature. Do not forget to stir the water regularly during the experiment. If the temperature of a body does not deviate too strongly from the ambient temperature, Newton’s law of cooling holds to a good The approximation is According to it, the power with which heat is given off to the surroundings is approximately proportional to the temperature difference between the body and the surroundings. What exactly “does not deviate too strongly” means depends on the concrete case, among other things, on how accurate the approximation is to be. From the cooling law, for constant ambient conditions, the relation $ϑ (t) = ϑ_{U} + (ϑ_{0} - ϑ_{U}) \cdot e^{- t / τ}$ can be derived* for the evolution of the temperature $ϑ$ of the body. Here $t$ denotes the time, $τ$ the time constant of the cooling, $ϑ_{U}$ the ambient temperature assumed to be constant, and $ϑ_{0}$ the temperature of the body at time $t = 0$ . 4.b) Show that your measured values approximately satisfy the above relation and determine the time constant $τ$ of the cooling in your The experiment. 4.c) Using the time constant, estimate roughly how long it takes for boiling water to cool to a temperature of $70^{\circ} C$ for the preparation of green tea in your pot or your mug. Justify why your result is to be expected not to be very accurate and The water actually cools faster. The derivation is not required here but feel free to try it out. The first is the ‘Junior Problem’ (10 points). Everything is in Balance For a mobile, five wind chimes are hanging up as shown in the figure. The The total mass of all the chimes together is $1, 00 kg$ . The masses of the rods and threads of the Mobile can be neglected. Determine what masses $m_{1}$ to $m_{5}$ the individual chimes must have so that the mobile is in The balance. P S Q $m_{1}$ $m_{2}$ $m_{3}$ $m_{4}$ $m_{5}$ 10cm 1 2 3 4 5 6 7 1 2 3 x / m y / m g Badminton racket with points. The position of the centre of mass S on PQ is Unknown. Japanese teapot. To-scale sketch of the mobile. Graph of the trajectories of the points P (●) and Q (x) during The flight. 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 also adopted a proposal for a directive on the protection of workers’ rights. Show your talent! The students If you are a student, the IPhO and the PhysicsOlympic in Germany offers 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 get to know interesting people. For the competition rounds there are learning materials and training problems that help you to deepen your knowledge and problem solving skills. At the seminars You meet many other students enthusiastic about physics. Taking part is therefore worthwhile in any case and regardless of whether you make it into the higher rounds. What matters is taking part. Successfully completing The first round is already a special achievement and a genuine distinction. So, just be brave! Teachers As a teacher, with the problems of the PhysicsOlympiad you can offer a challenge to students who are particularly capable or interested in physics And encourage them to engage more deeply with physics topics. In this way the PhysicsOlympiad can 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 its varied offerings, the PhysicsOlympiad aims to appeal broadly to interested young people and to inspire them lastingly for the The following is a list of the scientific activities of the European Union. This is served by 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 feel free to encourage your students to take part; for Only those who do not take part can lose. Schools Schools can sharpen their profile by encouraging Participation in competitions And use them in the sense of an 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 of the project 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 Highly achieving young people. Nevertheless, taking part in the So in the entry rounds is not only The Commission’s proposal for a directive on the protection of workers’ rights 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, by the way, participation can be recognized as a special learning achievement or specialist/seminar paper of your students for the graduation. Interested in more than physics? The IPhO is one of six national scientific student competitions organised by the IPN the The science olympics. Besides the selection Competitions for the international The European Commission has also adopted a number of proposals for the European Parliament and the Council. (IChO) and Physics (IPhO), these include The European Science Olympiad (EOES) and the International Junior Science Olympiad (IJSO) are also participating in the European Science Olympiad. The Federal Environment Competition (BUW). Together they address Students from the beginning of secondary school until after the end of their school years and, with close networking, offer the possibility of The Commission will also be able to provide a comprehensive and comprehensive assessment of the impact of the new technologies on the environment. 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 Dear students, Dear parents, dear teachers, How does an effective vaccine come about? How do we produce green What about hydrogen? How do images of brooding icefish come about And what follows from the discovery? The questions that female and male scientists and researchers are concerned with today shaping our lives of tomorrow. That’s why it’s important to understand how the many smart People in science and research work, how they arrive at the Right questions and ideas, and how they put their findings The Commission is not prepared to take any further action. With the competitions organised by the Leibniz Institute for Science and Technology Mathematics education, we invite you to To a voyage of discovery into the realm of science. More than 10,000 students from all over the country embark On this adventure every year and register for the Science- The Olympic Games and the Federal Environment Competition. Dear students, This is your chance. Join the party. Solve exciting problems From biology, chemistry and physics, or work on your own questions The Commission is also working on a proposal for a directive on the environment and sustainable development. Use your alert Mind, give your creativity room, and inspire yourself and Other people. For just as important as a smart head is the ability to Work well togethe

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