PROBLEMA n. 1 { T re ilindri molto s ivolosi 100 Pun ti In
gura a sinistra sono rappresen tati s hemati amen te tre ilindri uguali, ias uno di massa M , p osti su un piano orizzon tale on le basi v erti ali e omplanari e in mo do
he ias un ilindro abbia la sup er ie laterale tangen te a quelle degli altri due. I ilindri sono molto s iv olosi dato
he ogni forma di attrito fra tutte le sup er i a on tatto
e tras urabile. Allora, p er man tenere in equilibrio la struttura, v engono tese, una da una parte e una dall’altra { ome si v ede in
gura {, due orde inestensibili e di massa tras urabile
he ollegano gli assi dei due ilindri app oggiati sul piano. 1. Qual
e la minima tensione in ias una orda
he onsen te di man tenere in equilibrio il sistema? In seguito si mette in moto il sistema appli ando, al ilindro di sinistra, una forza ~ F , orizzon tale, ome mostrato nella
gura a destra, e subito dop o si eliminano le orde. 2. Qual
e l’in terv allo di v alori
he pu o assumere la forza
he a elera il sistema senza
he la struttura ollassi? |||||||||||
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Symmetry Argument Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Cylinder, String Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
The problem n. 1 { T re Other, of a kind used for the manufacture of goods Very much The following is the list of the countries of the European Union: 100 The Commission ti In
Gurus a Left I am representing Daddy s I will not be able to accept it. te three Other, of a kind used for the manufacture of goods equal, Ias one di Other M , p Other su un
- It ‘s not easy . The following is the list of the countries: such on le Basics v High wings e Other, of a kind used for the manufacture of goods e in mo do
he The Commission shall adopt a decision on the Other, of a kind used for the manufacture of goods have la Supplementary er ie Other, of a kind used for the manufacture of goods Other te a The other two of the Other Two. I Other, of a kind used for the manufacture of goods I am Very much s iv Other, of a kind used for the manufacture of goods given
he Each Form di Friction between All of them le Supplementary er i a on The touch
e I’m not sure. So, what? p er Man Hold in Balance la the structure, v The following is a list of the following: the theses, One of them. da One of them. Part e One of them. The other side { human beings si v Other in
Gurus {, two Other Other, of a kind used for the manufacture of goods e di Other Other
he other than The Commission Other, not further worked than hot-rolled of the two Other, of a kind used for the manufacture of goods App Other on the
- I’m not going to.
What
e la Minimum The following conditions shall apply: in Ias one Other
he onsen te di Man Hold in Balance il The system? In followed si It puts in Motorcycles il system the application of the code, al Other, of a kind used for the manufacture of goods di left, One of them.
- What ? ~ F , The following is the list of the countries: such, human beings shown In the
Gurus a Right, e Right now. after o si They eliminate le The Horde. 2. What
e l’in Other The following is the list of the di v Other
he pu o to hire la
- What ?
he Other, not further worked than cut il system without
he la structure What’s the matter? |||||||||||
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Symmetry Argument Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Cylinder, String Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
PROBLEMA n. 2 { T ri- i lo: : : termo dinami o 35 Pun ti La
gura rappresen ta un i lo termo dinami o ui
e sottop osto un sistema di n moli di un gas p erfetto monoatomi o. Il v olume del gas
e inizialmen te raddoppiato median te una trasformazione isoterma quasi stati a 1{2, e su essiv amen te viene rip ortato al v alore iniziale on una ompressione isobara quasi stati a 2{3. In ne, on un ris aldamen to duran te il quale il v olume rimane ostan te, il sistema viene rip ortato allo stato iniziale.
Cal olare il rendimen to di un’ip oteti a ma hina termi a
he segua questo i lo termo dinami o. ||||||||||| P ag. 2 di 4 AIF { Olimpiadi di Fisi a 2008 Ga ra Nazionale: PRO V A TEORICA { Senigallia { 18 Ap rile 2008
Topic: Thermodynamics Metodi: First Law of Thermodynamics, Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Mathematical Modeling, Physical Reasoning Objects: Gas, Heat Engine Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
The problem n. 2 { T ri- i lo: : : term Other, of a kind used for the manufacture of goods 35 The Commission ti La
Gurus representing ta un i lo term Other, of a kind used for the manufacture of goods ui
e The bottom Other un system di n Other di un Gas p of which: The following is the list of the monatomic atoms. Il v Other, of a kind used for the manufacture of foodstuffs of the Gas
e Initially te doubled Median te One of them. the transformation Other, of a kind used for the manufacture of goods Almost The following are the statistics: 1{2, e on the exiv I will not let you go. te He ‘s coming . RIP Other, not elsewhere specified or included al v Other Initial on One of them. Other, not further worked than hot-rolled Other, of a kind used for the manufacture of goods Almost The following are the statistics: 2{3. In ne, on un Other articles of heading No 5 to Durand te il which il v Other, of a kind used for the manufacture of foodstuffs It stays Other te, il system He ‘s coming . RIP Other, not elsewhere specified or included The following is the list of the State of the Union The first one.
Other il The Commission shall adopt implementing acts. to di un’ip The following is the list of ma Other Other
he following This one. i lo term I’m not going to say. ||||||||||| P ag. 2 di 4 The following information is provided: { The Olympics di The following is a list of 2008 Ga ra National team: The following is the list of the Member States: V A Theoretical { The following is the list of countries: { 18 Ap Reels 2008
Topic: Thermodynamics Metodi: First Law of Thermodynamics, Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Mathematical Modeling, Physical Reasoning Objects: Gas, Heat Engine Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
PROBLEMA n. 3 { Prove di elasti it
a 100 Pun ti In questo problema si vuole studiare, on un mo dello sempli ato, l’elasti it a di un materiale ristallino. Supp oniamo di a v ere un materiale
he, in assenza di forze esterne,
e ostituito di un reti olo ubi o di atomi,
he in teragis ono on un’energia p otenziale in teratomi a
he, al v ariare della distanza in teratomi a r , ha questa forma: U (r )
U 0 r 4 0 r 4 2 U 0 r 2 0 r 2 on U 0
5 eV; r 0
0:3 nm : P er sempli it a, si onsideri soltan to l’interazione di ias un atomo on i suoi viini pi
u prossimi; si tras uri quindi l’interazione fra gli atomi
he si tro v ano agli estremi di una diagonale del reti olo. Questa
e una sempli azione piuttosto drasti a p er h
e
e proprio l’in terazione oi se ondi vi ini
he tiene insieme il solido. 1. Si tra ino, in mo do qualitativ o e in funzione della distanza in teratomi a r , il gra o dell’energia p otenziale U (r ) e quello della relativ a forza di in terazione tra gli atomi vi ini f (r )
he pu o essere dedotto dal primo. 2. Si di a quan to v ale la distanza di equilibrio fra gli atomi, e a quali distanze la forza risulta attrattiv a o repulsiv a. Appli ando ad una fa ia del ristallo una forza di trazione p erp endi olare ad un piano reti olare, men tre la fa ia opp osta
e
ssata ad un supp orto, il ristallo si deforma, allungandosi nella direzione della forza. Sia F il mo dulo della forza, A l’area della sup er ie a ui la forza
e appli ata, L la lunghezza del ristallo nella direzione della forza, e L il suo allungamen to p er e etto della forza appli ata. Si
hiama \sforzo” la grandezza F
A e \deformazione” l’allungamen to relativ o L=L. Il rapp orto tra queste due grandezze, p er pi ole deformazioni,
e ostan te ed
e una aratteristi a del materiale nota ome \mo dulo di Y oung”: E
F
A L=L
: Si al oli: 3. il mo dulo di Y oung del materiale; 4. la deformazione quando il solido
e al pun to di rottura; 5. lo sforzo ne essario p er giungere alla rottura. Nota: Pu o essere utile ri ordare
he 1 1 + x
1 x quando x
||||||||||| P ag. 3 di 4 AIF { Olimpiadi di Fisi a 2008 Ga ra Nazionale: PRO V A TEORICA { Senigallia { 18 Ap rile 2008
Topic: Elasticity & Materials, Newtonian Mechanics Metodi: Stress-Strain Analysis, Hooke’s Law, Calculus-Integration, Approximation & Series Expansion Competenze: Mathematical Modeling, Diagrammatic Reasoning, Physical Reasoning Objects: Atom Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
The problem n. 3 { The evidence di You have it
a 100 The Commission ti In This one. The problem si He wants to studying, on un mo of the Other the act, The elastic it a di un Other materials I’m going to eat. Supp We are di a v The Commission un Other materials
he, in Absence di Forces the external,
e The Commission shall adopt implementing acts. di un Networks or di the atoms,
he in Other on a power source p The following information shall be provided: in The following table shows the results of the tests:
he, al v Airing of the distance in The following table shows the results of the tests: r , ha This one the form: U (r )
U 0 r 4 0 r 4 2 U 0 r 2 0 r 2 on U 0
5 eV; r 0
0:3 nm : P er Simplify it a, si Other Other to the interaction di The Commission shall adopt a decision on the atoms on i of its own wines pi
u the next; si Other So, what do you mean? the interaction between The Commission atoms
he si The Commission v
- What? to the Extreme di One of them. Other, not further worked than hot-rolled of the The Commission shall adopt implementing acts in accordance with Article 21 of this Regulation. This one
e One of them. Other Action I’m not sure. The Commission shall adopt implementing acts in accordance with Article 21 of this Regulation. p er h
e
e I mean, l’in Tanning oi If you go You know,
he It is together il It’s solid. 1. Si between the two, in mo do The quality o e in function of the distance in The following table shows the results of the tests: r , il The following is the list of the o Energy p The following information shall be provided: U (r ) e That one. of the Relative a
- What ? di in Tanning between The Commission atoms You know, f (r )
he pu o to be of which: from First of all. 2. Si di a When to v Other la distance di Balance between The Commission the atoms, e a which Distance la
- What ? The following is the list of the attractive a o Rejecting a. I ‘m going to go ad One of them. fa ia of the food One of them.
- What ? di Traction p Other Other, of a kind used for the manufacture of goods ad un
- It ‘s not easy . the wavelength of the network, Men and women three la fa ia Op. Other
e
Other ad un Supp the vegetable, il food si deformation, stretching out In the Direction of the
- I’m going to go. Both F il mo Other of the Come on, you guys. A the area of the Supplementary er ie a ui la
- What ?
e the following applies: L la length of the food In the Direction of the Come on, you guys. e L il his Other to p er e Other of the
- What ? The Commission shall adopt implementing acts. Si
Other I’m trying. la size F
A e ‘deformation’ the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of the length of to Relative o L=L. Il REP vegetable between These two the greatness, p er Other deformities,
e Other te ed
e One of them. characteristics of a of the Other materials Notes human beings \mo Other di Y the following: E
F
A L=L
: Si for oil: 3. il mo Other di Y Oung of the the material; 4. la Deformation When il Other, not further worked than hot-rolled
e al the following points are added: to di the breakdown; 5. lo The amount of effort I am not p er to arrive to the The first is the breakdown. Note: Pu o to be Useful Re-order
he 1 1 + x
1 x When x
||||||||||| P ag. 3 di 4 The following information is provided: { The Olympics di The following is a list of 2008 Ga ra National team: The following is the list of the Member States: V A Theoretical { The following is the list of countries: { 18 Ap Reels 2008
Topic: Elasticity & Materials, Newtonian Mechanics Metodi: Stress-Strain Analysis, Hooke’s Law, Calculus-Integration, Approximation & Series Expansion Competenze: Mathematical Modeling, Diagrammatic Reasoning, Physical Reasoning Objects: Atom Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
PROBLEMA n. 4 { Condensato ri semp re pi
u pi oli 65 Pun ti La apa it a di un ondensatore in ui lo sp essore d del dielettri o sia molto pi olo risp etto alle dimensioni delle armature (la ondizione pu o essere p osta ome d 2
S , essendo S la sup er ie delle armature) pu o essere sempre al olata ome quella di un ondensatore a fa e piane e parallele. 1. Dop o a v er determinato l’espressione della apa it a di un ondensatore sferi o nel vuoto (” r
le ui armature abbiano raggi R 1 e R 2 , v eri are la pre eden te asserzione, quando sia so ddisfatta la ondizione R 2 R 1
R 1 . Si onsideri ora un ondensatore (p er il quale la ondizione detta sia v eri ata, osi h
e p ossa essere assimilato ad un ondensatore piano) in ui met a del v olume sia ostituito dalle armature e met a dal materiale isolan te aratterizzato dalla ostan te dielettri a relativ a (” r
e dalla rigidit a dielettri a (E m ) de nita ome il massimo amp o elettri o
he il dielettri o pu o sopp ortare senza
he v enga attra v ersato { e quindi distrutto { da una s ari a. Un ondensatore
e a sua v olta individuato da due parametri aratteristi i: la apa it a C e la tensione massima di la v oro V max . N.B. P er non onfondere la tensione, io
e la d.d.p. V appli ata tra le armature on il v olume del ondensatore, quest’ultimo sar a indi ato { in mo do in usuale { on la lettera . 2. Mostrare
he il v olume
di un ondensatore di apa it a C e tensione massima di la v oro V max , non pu o essere inferiore ad un minimo. T ro v are
min in funzione delle due propriet a aratteristi he del dielettri o ” r e E m . 3. Quali dei seguen ti materiali dielettri i onsen tirebb e di pro durre ondensatori di v olume minimo? Materiale ” r E m [ kV/mm ℄ 1. Carta paraÆnata 2:5 50 2. Cerami a 60 15 3. Mi a 8 90 4. P olistirolo 2:6 50 5. P or ellana 6 25 6. Resina ep ossidi a 4 35 7. T e on 2:2 20 NOT A: I dati rip ortati in tab ella sono puramen te indi ativi e in al uni asi si riferis ono a parti olari ampioni dei div ersi materiali; p er esempio v ari tipi di resine o di erami he p ossono a v ere aratteristi he notev olmen te div erse da quelle indi ate qui. 4. T ra quelli rip ortati sopra, quale dielettri o si pu o ritenere sia stato usato p er realizzare un ondensatore da 4:7 F
he sopp orta una tensione di la v oro di 50 V ed ha la forma di un pi olo parallelepip edo di 10
10
2 mm 3 ? Materiale pro dotto dal grupp o OLIMPIADI PROGETTO PROGETTO OLIMPIADI Segreteria Olimpiadi Italiane della Fisi a p resso Li eo S ienti o \U. Mo rin”, MESTRE (VE) fax: 041.584.1272 e-mail: olifis libero.it P ag. 4 di 4
Topic: Electrostatics Metodi: Gauss’s Law, Electric Potential Method, Experimental Data Analysis Competenze: Mathematical Modeling, Physical Reasoning, Estimation & Approximation Objects: Capacitor Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
The problem n. 4 { Other, of a kind used for the manufacture of goods ri The Commission shall adopt the following: re pi
u Other oils 65 The Commission ti La
- What? a di un Other, of a kind used for the manufacture of goods in ui lo sp The following is the list of the countries of the European Union: d of the a width of not more than 15 mm It’s either Very much Other Responsibility Other The Commission Size of the Other articles of iron or steel (la the condition pu o to be p Other human beings d 2
S , being S la Supplementary er ie of the (including armor) pu o to be Always Other, of a kind used for the manufacture of goods of heading 8106 human beings That one. di un Other, of a kind used for the manufacture of goods a fa e Plans e parallel to the other. 1. After o a v er determined the expression of the
- What? a di un Other, of a kind used for the manufacture of goods spheres or In the empty (” r =
le ui Other articles of iron or steel Have Radiation R 1 e R 2 , v You were are la for Eden te the claim, When It’s either so Other, of a kind used for the manufacture of goods la the condition R 2 R 1
R 1 . Si Other Now un Other, of a kind used for the manufacture of goods (p er il which la the condition the following: It’s either v You were the following: Other h
e p Other to be the product is not ad un Other, of a kind used for the manufacture of goods (Please) in ui The Commission a of the v Other, of a kind used for the manufacture of foodstuffs It’s either The Commission shall adopt implementing acts. from Other articles of iron or steel e The Commission a from Other materials isolan te Other, of a width of not more than 30 mm from Other te Other, of a kind used for the manufacture of goods Relative a (” r
e from Rigid a Other, of a kind used for the manufacture of goods (E m ) de Notwithstanding human beings il Not more than amp o electrical or
he il a width of not more than 15 mm pu o Other toasting without
he v The following is the list of the products: the following points are added: v Other { e So, what do you mean? Destroyed { da One of them. The following is the list of the countries of the European Union: Un Other, of a kind used for the manufacture of goods
e a his v
- I’m not going to. identified da two Parameters characteristics i: la
- What? a C e la The following conditions shall apply: maximum di la v gold V Max . N.B. P er Not Flooding la the voltage, io
e la d.d.p. V Applications for the between le Other articles of iron or steel on il v Other, of a kind used for the manufacture of foodstuffs of the a winding machine, The latter will be a Other { in mo do in common { on la Letter . 2. Show
he il v Other, of a kind used for the manufacture of foodstuffs
di un Other, of a kind used for the manufacture of goods di
- What? a C e The following conditions shall apply: maximum di la v gold V Max , Not pu o to be Other ad un I’m not sure. T ro v are
Minimum number of days in function of the two Property a Other he of the a width of not more than 15 mm ” r e E m . 3. What of the following ti Other materials the following table shows the following: onsen The following is the list of the countries of the European Union: e di for
- to be painful Other, of a kind used for the manufacture of goods di v Other, of a kind used for the manufacture of foodstuffs What’s the minimum? Other materials ” r E m [ kV/mm ℄
Paper
- The first 2:5 50
Look at me 60 15 3. Mi a 8 90 4. P Other, of a thickness of not more than 10 mm 2:6 50 5. P or ellana 6 25 6. Other, of a kind used for the manufacture of goods ep Other, of a kind used for the manufacture of goods 4 35 7. T e on 2:2 20 Not A: I data RIP Other articles of heading No. in tab She ‘s a I am Puramins te active e in to the one Other si Reported on a Other, of a kind used for the manufacture of goods Other of the Div Other materials; p er Example v Other Type of goods di Other, of a kind used for the manufacture of goods o di I was he p They are a v The following are the Other he I’m not sure. Other te Div Other da The other two Other I’m going to get you here. 4. T ra The other RIP Other articles of heading No. above, which a width of not more than 15 mm si pu o to hold It’s either State of the Union used p er The Commission shall adopt the following measures: un Other, of a kind used for the manufacture of goods da 4:7 F
he Other Other One of them. The following conditions shall apply: di la v gold di 50 V ed ha la Form di un Other Other
- The following: di 10
10
2 mm 3 ? Other materials for The Commission from Group o Olympic Games Project Project Olympic Games The Secretariat The Olympics Italian of the The following is a list of p Results Li eo The Commission o \U. Mo the following paragraphs are added: The Master (VE) The fax: 041.584.1272 E-mail: The following information is provided by: P ag. 4 di 4
Topic: Electrostatics Metodi: Gauss’s Law, Electric Potential Method, Experimental Data Analysis Competenze: Mathematical Modeling, Physical Reasoning, Estimation & Approximation Objects: Capacitor Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)