PROBLEMA n. 1 { Equilib rismi: : : 100 Pun ti Quesito n. 1. In assenza di attriti, le forze appli ate al blo o di massa m 2 sono: il p eso (v erti ale), la reazione vin olare ~ N dal piano orizzon tale (v erti ale), la reazione vin olare ~ N 0 da parte del blo o di massa m 1 (obliqua) e la forza ~ F (orizzon tale). Le forze appli ate al blo o di massa m 1 sono: il p eso (v erti ale), la reazione vin olare ~ N 00 dal piano v erti ale (orizzon tale), la reazione vin olare ~ N 0 da parte del blo o di massa m 2 (obliqua).
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Kinematic Equations Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
The problem n. 1 { Balance of payments He laughs: : : 100 The Commission ti Question No n. 1. In Absence di the friction, le Forces Other al The Commission o di Other m 2 are: il p That’s it. (v high-winged, la reaction wines of the type described in this chapter ~ N from
- It ‘s not easy . The following is the list of the countries: such (v high-winged, la reaction wines of the type described in this chapter ~ N 0 da Part of the The Commission o di Other m 1 (Officials) e la
- What ? ~ F (horizon) The Commission has not yet taken a decision. Le Forces Other al The Commission o di Other m 1 are: il p That’s it. (v high-winged, la reaction wines of the type described in this chapter ~ N 00 from
- It ‘s not easy . v High-winged (horizon) the following: la reaction wines of the type described in this chapter ~ N 0 da Part of the The Commission o di Other m 2 (Officials are deleted)
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Kinematic Equations Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
Quesito n. 2. All’equilibrio le forze su ias un blo o dev ono a v ere risultan te n ulla. In omp onen ti, prendendo l’asse x orizzon tale da sinistra a destra e l’asse y v erti ale dal basso v erso l’alto, e indi ando on F 0 l’in tensit a di ~ F in ondizioni di equilibrio, si ha: F 0 N 0 sen
= 0 N m 2 g N 0 os
= 0 N 0 sen
N 00
0 N 0 os
m 1 g
0 Dalla prima e la quarta di queste equazioni, on fa ili sostituzioni, si ha N 0
m 1 g os
F 0
m 1 g tan
= 28:3 N
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Conservation Laws Competenze: Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
Question No n. 2. The Balance le Forces su The Commission shall adopt a decision on the The Commission o It must be The Commission a v The Commission Resultan te n I’m going to see you. In The Commission shall adopt implementing acts. Other ti, taking the axis x The following is the list of the countries: such da Left a Right e the axis y v High-winged from Low v Other The high, e Indians on F 0 l’in Tensile a di ~ F in Other articles of heading No. di the balance, si ha: F 0 N 0 Other
= 0 N m 2 g N 0 os
= 0 N 0 Other
N 00
0 N 0 os
m 1 g
0 From her . Before e la Fourth di These the equations, on He does them. replacements, si ha N 0
m 1 g os
F 0
m 1 g Other
= 28:3 N
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Conservation Laws Competenze: Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
Quesito n. 3. Con una forza maggiore, pari a 2F 0 , non si ha pi
u equilibrio; il orp o di massa m 2 si m uo v e on a elerazione a 2 orizzon tale e il orp o di massa m 1 si m uo v e on a elerazione a 1 v erti ale. Le equazioni pre eden ti, p ertan to, si mo di ano os
: 2F 0 N 0 sen
= m 2 a 2 N m 2 g N 0 os
= 0 N 0 sen
N 00
0 N 0 os
m 1 g
m 1 a 1 P ag. 1 AIF { Olimpiadi di Fisi a Ga ra Nazionale: SOLUZIONE della Prova T eo ri a { Senigallia { 18 Ap rile 2007 Inoltre, p er onsiderazioni geometri he, fra gli sp ostamen ti, e quindi le a elerazioni, dei due blo
hi v ale la relazione a 1 : a 2
sen
: os
, io
e a 2
a 1
tan
. Sostituendo nella prima e quarta equazione qui sopra, si ri a v a: N 0
2F 0 sen
m 2 a 1 sen
tan
= 2m 1 g os
m 2 a 1 sen
tan
a 1
N 0 os
m 1 g
g m 2 a 1 m 1 tan 2
a 1
g m 1 tan 2
m 1 tan 2
m 2
3:50 m s 2
Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Vector Decomposition, Kinematic Equations Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
Question No n. 3. With One of them.
- What ? the major, equal a 2F 0 , Not si ha pi
u the balance; il orp o di Other m 2 si m uo v e on Other, of a kind used for the manufacture of goods a 2 The following is the list of the countries: such e il orp o di Other m 1 si m uo v e on Other, of a kind used for the manufacture of goods a 1 v high wings. Le Equations for Eden ti, p Other to, si mo di
- What? os
: 2F 0 N 0 Other
= m 2 a 2 N m 2 g N 0 os
= 0 N 0 Other
N 00
0 N 0 os
m 1 g
m 1 a 1 P ag. 1 The following information is provided: { The Olympics di The following is a list of Ga ra National team: The Commission of the Try it . T eo ri a { The following is the list of countries: { 18 Ap Reels 2007 Besides, p er The Commission shall adopt the following measures: Other geometric he, between The Commission sp Other articles of heading No. ti, e So, what do you mean? le with a height of of the two The Commission
hi v Other la Report by the Commission a 1 : a 2
Other
: os
, io
e a 2
a 1
Other
. Substituting In the Before e Fourth Equation Here . above, si ri a v a: N 0
2F 0 Other
m 2 a 1 Other
Other
= 2m 1 g os
m 2 a 1 Other
Other
a 1
N 0 os
m 1 g
g m 2 a 1 m 1 Other 2
a 1
g m 1 Other 2
m 1 Other 2
m 2
3:50 m s 2
Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Vector Decomposition, Kinematic Equations Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)
Quesito n. 4. Il blo o di massa m 2 ha un’a elerazione a 2
a 1
tan
e p ertan to, a partire dall’istan te t
0 in ui la forza ~ F raddoppia l’in tensit a, ha una v elo it a v
a 2 t. La p otenza da appli are, p ertan to,
e W
2F 0 v
2m 1 g a 1 t. Essa res e linearmen te nel temp o on un o eÆ ien te 2m 1 g a 1
344 W s 1 . Nota: Sostituendo ad a 1 il v alore gi a arrotondato, os
ome
e stato rip ortato sopra al pun to 3, si otterrebb e W =t
343 W s 1
he
e ugualmen te a ettabile.
Topic: Newtonian Mechanics, Conservation of Energy Metodi: Kinematic Equations, Free-Body Diagram, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Question No n. 4. Il The Commission o di Other m 2 ha a heating a 2
a 1
Other
e p Other to, a to leave from the Istan te t
0 in ui la
- What ? ~ F doubled l’in Tensile a, ha One of them. v I’m going to it a v = a 2 t. La p the authorisation da the application is, p Other to,
e W
2F 0 v
2m 1 g a 1 t. It Res and Linearmen te In the Temp o on un o It is te 2m 1 g a 1
344 W s 1 . Note: Substituting ad a 1 il v Other gi a rounded, os
human beings
e State of the Union RIP Other, not elsewhere specified or included above al the following points are added: to 3, si Other e W =t
343 W s 1
he
e The following is a list of the te The Commission shall adopt implementing acts in accordance with Article 21 of this Regulation.
Topic: Newtonian Mechanics, Conservation of Energy Metodi: Kinematic Equations, Free-Body Diagram, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Quesito n. 5. In presenza di forze di attrito, ~ A e ~ A 00 (risp ettiv amen te), sulle sup er i orizzon tale e v erti ale
he si aggiungono alle altre forze gi a onsiderate, la forza F minima p er ottenere l’equilibrio dev’essere minore di F 0 , p er ui l’attrito orizzon tale dev’essere riv olto nel v erso p ositiv o delle x p er osta olare il moto del blo o di massa m 2 v erso sinistra, e quello v erti ale v erso l’alto p er osta olare il moto del blo o di massa m 1 v erso il basso, moti
he si a vrebb ero in assenza di ~ F e di attriti. Quindi le equazioni pre eden ti si mo di ano os
: F + A N 0 sen
= 0 N m 2 g N 0 os
= 0 N 0 sen
N 00
0 N 0 os
A 00 m 1 g
0 I v alori massimi p ossibili di A e A 00 sono risp ettiv amen te A
N e A 00
N 00 . Indi hiamo i loro v alori e ettivi on A
N e A 00
00 N 00 . Questa v olta serv ono tutte e quattro le equazioni pre eden ti; si ri a v a N 00
N 0 sen
N 0 os
00 N 0 sen
m 1 g
0 ) N 0
m 1 g os
00 sen
N
m 1 os
os
00 sen
m 2
g F
m 1 sen
(m 1 + m 2 ) os
00 m 2 sen
os
00 sen
g Il v alore di F de res e in mo do monotono al res ere sia di
he di
00 , p er ui p er minimizzare F ( n h
e esso
e p ositiv o, naturalmen te) o orre assumere i v alori massimi p ossibili sia di
he di
00 . L’ultima form ula diviene p ertan to: F min
m 1 sen
(m 1 + m 2 ) os
2 m 2 sen
os
sen
g
10:7 N P ag. 2 AIF { Olimpiadi di Fisi a Ga ra Nazionale: SOLUZIONE della Prova T eo ri a { Senigallia { 18 Ap rile 2007 PROBLEMA n. 2 { O hio alle induttanze! 50 Pun ti
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Physical Modeling Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Question No n. 5. In the presence di Forces di the friction, ~ A e ~ A 00 (resp. Other I will not let you go. te), on the Supplementary er i The following is the list of the countries: such e v High-winged
he si add The Commission Other Forces gi a and unseen, la
- What ? F Minimum p er to obtain The balance It must be Minor di F 0 , p er ui the friction The following is the list of the countries: such It must be The following is the list of the countries of the European Union: I’m going to In the v Other p Other o of the x p er Other, of a kind used for the manufacture of goods il Motorcycles of the The Commission o di Other m 2 v Other left, e That one. v High-winged v Other The high p er Other, of a kind used for the manufacture of goods il Motorcycles of the The Commission o di Other m 1 v Other il low, Motives
he si a The Commission shall adopt implementing acts. I was in Absence di ~ F e di I’m not going to. So, what? le Equations for Eden ti si mo di
- What? os
: F + A N 0 Other
= 0 N m 2 g N 0 os
= 0 N 0 Other
N 00
0 N 0 os
A 00 m 1 g
0 I v Other Maximum p Other, of a kind used for the manufacture of goods di A e A 00 I am Responsibility Other I will not let you go. te A
N e A 00
N 00 . Indians I ‘m going to go . i They v Other e Other on A
N e A 00
00 N 00 . This one v
- I’m not going to. Serving The Commission All of them e four le Equations for Eden ti; si ri a v a N 00 = N 0 Other
N 0 os
00 N 0 Other
m 1 g
0 ) N 0
m 1 g os
00 Other
N
m 1 os
os
00 Other
m 2
g F
m 1 Other
(m 1 + m 2 ) os
00 m 2 Other
os
00 Other
g Il v Other di F of res and in mo do The following is a list of the categories of products used: al Other It’s either di
he di
00 , p er ui p er Minimize the F ( n h
e It
e p Other o, Natural products te) o Horrors to hire i v Other Maximum p Other, of a kind used for the manufacture of goods It’s either di
he di
00 . The last one. form The Commission shall adopt a decision on the It becomes p Other to: F Minimum number of days
m 1 Other
(m 1 + m 2 ) os
2 m 2 Other
os
Other
g
10:7 N P ag. 2 The following information is provided: { The Olympics di The following Ga ra National team: The Commission of the Try it . T eo ri a { The following is the list of countries: { 18 Ap Reels 2007 The problem n. 2 { Oh, yeah. The Commission I’m not going to lie. 50 The Commission ti
Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition, Physical Modeling Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.2 Soluzione: Soluzioni (PDF)
Quesito n. 1. Alla
hiusura dell’in terruttore la orren te p er l’induttanza si man tiene istan taneamen te n ulla e l’equazione della maglia attiv a d a 3R I 0
E ) E
3 (2:5 k
) (5 mA)
37:5 V A regime in v e e la f.e.m. ai api dell’induttanza
e n ulla, dunque la resistenza vista dal generatore
e R ?
R + (R 2 k R 1 ) ; p er ui l’equazione del ir uito equiv alen te d a R ? I 1
E )
R + 2R R 1 2R + R 1
I 1
2R 2 + 3R R 1 2R + R 1 I 1
2R + 3R 1 2R + R 1 R I 1
E
he, sostituendo l’espressione pre eden te di E , si ridu e a (2R + 3R 1 )I 1
3 (2R + R 1 )I 0 ) 3 (I 1 I 0 ) R 1
2 (3I 0 I 1 ) R da ui R 1
2 (3I 0 I 1 ) 3 (I 1 I 0 ) R
2 (15 9) mA 3 (9 5) mA R
R
2:5 k
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction, Physical Modeling Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Inductor, Resistor, Switch, Battery Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Question No n. 1. At the
Other, of a kind used for the manufacture of goods of the in The terror la Other articles te p er the inductance si Man It is Other The Commission shall adopt the following measures: te n The following is the list of the products: e The equation of the T-shirt active a d a 3R I 0
E ) E
3 (2:5 k
) (5 mA)
37:5 V A the scheme in v e e la f.e.m. ai Bees of induction
e n the following: So, what? la resistance view from Manufacture of electrical equipment
e R ?
R + (R 2 k R 1 ) ; p er ui The equation of the I have forgotten Equivalent to Other te d a R ? I 1
E )
R + 2R R 1 2R + R 1
I 1
2R 2 + 3R R 1 2R + R 1 I 1
2R + 3R 1 2R + R 1 R I 1
E
he, by replacing the expression for Eden te di E , si Reducing and a (2R + 3R 1 )I 1
3 (2R + R 1 )I 0 ) 3 (I 1 I 0 ) R 1
2 (3I 0 I 1 ) R da ui R 1
2 (3I 0 I 1 ) 3 (I 1 I 0 ) R
2 (15 9) mA 3 (9 5) mA R
R
2:5 k
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction, Physical Modeling Competenze: Diagrammatic Reasoning, Mathematical Modeling, Physical Reasoning Objects: Inductor, Resistor, Switch, Battery Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Quesito n. 2. L’energia magneti a immagazzinata nel ir uito
e U L
1
2 LI 2 L , essendo I L la orren te nel ramo dell’induttanza. A regime la d.d.p. ai api dell’induttanza
e n ulla e dunque basta onsiderare il parallelo delle resistenze R 1
R ed R 2
2R : ne segue immediatamen te
he la orren te in R 1
e doppia dell’altra e pari a 2/3 della orren te totale. Pi
u formalmen te tale orren te
e determinata dalle equazioni (dette del partitore di orren te): ( I L + I R 2
I 1 R I L
2R I R 2 ) I L
2R 3R I 1
2 3 I 1
6 mA App ena riap erto l’in terruttore l’energia magneti a viene dissipata dalle resistenze R 1 ed R 2 , in parti prop orzionali ai v alori delle due resistenze, dato
he la orren te
e la stessa in ogni pun to della maglia: dunque W 1
R 1 I 2 ; W 2
R 2 I 2 . Nella resistenza R 1 si dissipa quindi 1/3 dell’energia imagazzinata: dunque U
1 3 U L
1 3 1 2 L I 2 L ) L
6U I 2 L
6:67 mH
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning, Diagrammatic Reasoning Objects: Inductor, Resistor, Switch Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Question No n. 2. Energy Magnetic Stored In the I have forgotten
e U L
1
2 LI 2 L , being I L la Other articles te In the Branch The Commission has already adopted a proposal for a directive on the protection of workers’ rights. A the scheme la d.d.p. ai Bees of induction
e n The following is the list of the products: e So, what? That ‘s enough . to be considered il Other of the Resistance R 1
R ed R 2
2R : ne follows Immediate te
he la Other articles te in R 1
e double of the other e equal a 2/3 of the Other articles te The total. Pi
u Formal te such Other articles te
e determined from Equations (debt) of the Scorer di Other articles te): ( I L + I R 2
I 1 R I L
2R I R 2 ) I L
2R 3R I 1
2 3 I 1
6 mA App Other Other high l’in The terror energy Magnetic He ‘s coming . Dispersed from Resistance R 1 ed R 2 , in Parts Prop Other, of a kind used for the manufacture of goods ai v Other of the two resistance, given
he la Other articles te
e la itself in Each the following points are added: to of the T-shirt: So, what? W 1
R 1 I 2 ; W 2
R 2 I 2 . In the resistance R 1 si
- What? So, what do you mean? 1/3 energy The following is the list of the following: So, what? U = 1 3 U L = 1 3 1 2 L I 2 L ) L = 6U I 2 L = 6:67 mH
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning, Diagrammatic Reasoning Objects: Inductor, Resistor, Switch Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Quesito n. 3. La tensione ai api dell’induttanza, V L , app ena si apre il ir uito, quando la orren te
e I L si determina dall’equazione di maglia (2R + R 1 )I L V L
0 ) V L
3R I L
3 (2:5 k
) (6 mA)
45 V
he
e maggiore della f.e.m. del generatore. Osserv azione: Nel aso in esame, on R 2
2R , si ha
he V L
(2R + R 1 ) I L
(2R + R 1 ) 2R 2R + R 1 I 1
2R I 1 men tre si
e visto
he E
2R + 3R 1 2R + R 1 R I 1 La ondizione su R 1 p er ui sar a V L
E all’ap ertura del ir uito
e data da V L E
2 (2R + R 1 ) 2R + 3R 1
1 ) R 1 < 2R P ag. 3 AIF { Olimpiadi di Fisi a Ga ra Nazionale: SOLUZIONE della Prova T eo ri a { Senigallia { 18 Ap rile 2007 PROBLEMA n. 3 { Che aldo quest’estate! 100 Pun ti
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Faraday’s Law of Induction, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Inductor, Resistor, Switch Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Question No n. 3. La The following conditions shall apply: ai Bees of induction, V L , App Other si It opens. il I will forget, When la Other articles te
e I L si determines the from the equation di T-shirt (2R + R 1 )I L V L
0 ) V L
3R I L
3 (2:5 k
) (6 mA)
45 V
he
e major of the f.e.m. of the The generator. The Commission shall adopt implementing acts. Action: In the Other in the examination, on R 2
2R , si ha
he V L
(2R + R 1 ) I L
(2R + R 1 ) 2R 2R + R 1 I 1
2R I 1 Men and women three si
e See also
he E
2R + 3R 1 2R + R 1 R I 1 La the condition su R 1 p er ui will be a V L
E to the ap Other, of a kind used for the manufacture of goods of the I have forgotten
e Date of the date da V L E
2 (2R + R 1 ) 2R + 3R 1
1 ) R 1 < 2R P ag. 3 The following information is provided: { The Olympics di The following is a list of Ga ra National team: The Commission of the Try it . T eo ri a { The following is the list of countries: { 18 Ap Reels 2007 The problem n. 3 { That Other This summer! 100 The Commission ti
Topic: Circuits, Electromagnetic Induction Metodi: Kirchhoff’s Laws, Faraday’s Law of Induction, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Inductor, Resistor, Switch Fonte: Testo (PDF) — p.3 Soluzione: Soluzioni (PDF)
Quesito n. 1. Il
usso di energia
he en tra nell’appartamen to, sotto forma di alore, p er onduzione
e dato da
in
K ( T e T ). Il
usso di energia
he il ondizionatore estrae dall’appartamen to
e dato da
out
” P do v e ”
e l’eÆ ienza di un frigorifero ideale ( io
e di un frigorifero
he utilizza il i lo di Carnot). Dal momen to
he il ondizionatore funziona tra due sorgen ti, l’appartamen to a temp eratura T e l’am bien te esterno a temp eratura T e , l’eÆ ienza di un frigorifero di Carnot
he funziona tra le stesse sorgen ti
e data da ”
T =(T e T ) p er ui, ri omp onendo la relazione del
usso in us ita, si ha
out
T T e T P
Topic: Thermodynamics, Conservation of Energy Metodi: Thermodynamic Cycle Analysis, First Law of Thermodynamics, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Question No n. 1. Il
the outer di energy
he en between In the apartment to, below Form di Then, p er Other, of a kind used for the manufacture of goods
e given da
in
K ( T e T ). Il
the outer di energy
he il Other, of a kind used for the manufacture of goods Mining from the apartment to
e given da
out
” P do v e ”
e The Commission shall adopt a decision on the di un Other, of a kind used for the manufacture of refrigerators Ideal ( io
e di un Other, of a kind used for the manufacture of refrigerators
he use il i lo di Carnot . From Moments to
he il Other, of a kind used for the manufacture of goods It works . between two Other ti, the apartment to a Temp Other T e l’am All right, all right. te Other a Temp Other T e , The Commission shall adopt a decision on the di un Other, of a kind used for the manufacture of refrigerators di Other meat offal
he It works . between le The same Other ti
e Date of the date da ”
T =(T e T ) p er ui, Other by the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight of the weight la Report by the Commission of the
the outer in the United States, si ha
out
T T e T P
Topic: Thermodynamics, Conservation of Energy Metodi: Thermodynamic Cycle Analysis, First Law of Thermodynamics, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Quesito n. 2. In ondizioni stazionarie, il
usso in ingresso
e uguale al
usso in us ita. Dunque si ha K (T e T )
T T e T P K T 2 (2K T e +
P ) T + K T 2 e
0 ) T 2 (2T e +
) T + T 2 e
0 on T e
305 K e a v endo p osto
=
P =K
0:84 K. T
2 T e +
p 4 T e
2 2 Delle due radi i, una sola
e minore della temp eratura esterna, p er ui si ha T
289 K
16 Æ C.
Topic: Thermodynamics, Conservation of Energy Metodi: Thermodynamic Cycle Analysis, First Law of Thermodynamics, Differential Equations Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Question No n. 2. In Other articles of heading No. stationary, il
the outer in The entry
e equal to al
the outer in The United States. So, what? si ha K (T e T )
T T e T P K T 2 (2K T e +
P ) T + K T 2 e
0 ) T 2 (2T e +
) T + T 2 e
0 on T e
305 K e a v Other p Other
=
P =K
0:84 K. T
2 T e +
p 4 T e
2 2 Of the following: two the radius i, One of them. alone
e Minor of the Temp Other the external, p er ui si ha T
289 K
16 Æ C.
Topic: Thermodynamics, Conservation of Energy Metodi: Thermodynamic Cycle Analysis, First Law of Thermodynamics, Differential Equations Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Quesito n. 3. Quando si sp egne il ondizionatore d’aria ’
e soltan to il
usso di energia dall’esterno v erso l’in terno dell’appartamen to. Si ha Q t
K ( T e T (t)) e Q
C T Ad ogni in terv allo di temp o t, si ha una v ariazione di temp eratura data da T
(T e T ) t a v endo p osto
= K =C : Con questa espressione, partendo dal v alore iniziale di (T e T ), si p ossono al olare T e T ogni 15 min uti , ome mostrato nella seguen te tab ella. T emp o t [min℄ T e T (t) [ Æ C℄ T [ Æ C℄ T (t) [ Æ C℄ 0 18.0 15 14.0 3.4 21.4 30 10.6 2.6 24.0 45 8.0 1.9 25.9 60 6.1 1.5 27.4 La temp eratura (approssimata) dell’appartamen to dop o un’ora
e di 27:4 Æ C.
Topic: Thermodynamics, Conservation of Energy Metodi: First Law of Thermodynamics, Differential Equations, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning, Estimation & Approximation Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Question No n. 3. When si sp Other il Other, of a kind used for the manufacture of goods Air ’
e Other to il
the outer di energy from the outside v Other l’in Other of the apartment to. Si ha Q t
K ( T e T (t)) e Q
C T Ad Each in Other The following is the list of the di Temp o t, si ha One of them. v Air conditioning di Temp Other Date of the date da T
(T e T ) t a v Other p Other
= K =C : With This one the expression, I ‘m leaving from v Other Initial di (T e T ), si p They are in the waves T e T Each 15 Minimum number of days Other , human beings shown In the following te tab She’s the one. T The Commission o t [min] T e T (t) [ Æ C℄ T [ Æ C℄ T (t) [ Æ C℄ 0 18.0 15 14.0 3.4 21.4 30 10.6 2.6 24.0 45 8.0 1.9 25.9 60 6.1 1.5 27.4 La Temp Other (Approach) of the apartment to after o an hour
e di 27:4 Æ C.
Topic: Thermodynamics, Conservation of Energy Metodi: First Law of Thermodynamics, Differential Equations, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning, Estimation & Approximation Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Quesito n. 4. Si onsiderino due termini onse utivi della su essione: F k
T e T (t k ) e il seguen te F k +1
T e T (t k +1 ) Op erando ome sopra, si pu o s riv ere
he T (t k +1 ) T (t k )
T
[T e T (t k )℄ t o vv ero, sostituendo in termini di F k e F k +1 (T e F k +1 ) (T e F k )
F k F k +1
F k t ) F k +1
(1
t) F k ) F k +1 F k
1
t P ag. 4 AIF { Olimpiadi di Fisi a Ga ra Nazionale: SOLUZIONE della Prova T eo ri a { Senigallia { 18 Ap rile 2007 La su essione F k
e quindi una progressione geometri a di ragione ( 1
t) p er ui F (t k )
F (t 0 ) (1
t) k ) T e T (t k )
(T e T 0 ) ( 1
t) k
Topic: Thermodynamics Metodi: Differential Equations, Approximation & Series Expansion, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Question No n. 4. Si Other, not further worked than cutting two the terms Useful of the by way of derogation: F k
T e T (t k ) e il following te F k +1
T e T (t k +1 ) Op by the time human beings above, si pu o The following is the list of the The Commission
he T (t k +1 ) T (t k )
T
[T e T (t k )℄ t o vv I was, by replacing in the terms di F k e F k +1 (T e F k +1 ) (T e F k )
F k F k +1
F k t ) F k +1
(1
t) F k ) F k +1 F k
1
t P ag. 4 The following information is provided: { The Olympics di The following is a list of Ga ra National team: The Commission of the Try it . T eo ri a { The following is the list of countries: { 18 Ap Reels 2007 La on exemption F k
e So, what do you mean? One of them. The following is the list of the following: Geometers a di Right ( 1
t) p er ui F (t k )
F (t 0 ) (1
t) k ) T e T (t k )
(T e T 0 ) ( 1
t) k
Topic: Thermodynamics Metodi: Differential Equations, Approximation & Series Expansion, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.4 Soluzione: Soluzioni (PDF)
Quesito n. 5. Si p one adesso t
t=n e dop o n in remen ti temp orali, io
e al temp o t si ha F (t n )
T e T (t n )
(T e T 0 )
1
t n
n P er n ! 1 p osto x
n
t si ha
he x ! 1, e i si ri ondu e al limite notev ole lim x! 1
1 + 1 x
x
e : Infatti F (t)
T e T (t)
lim x! 1 (T e T 0 )
1 + 1 x
t x
(T e T 0 ) lim x! 1
1 + 1 x
x
t
(T e T 0 ) e
t
Topic: Thermodynamics Metodi: Differential Equations, Approximation & Series Expansion, Calculus-Integration Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Question No n. 5. Si p One Now t
t=n e after o n in remen ti Temp oral, io
e al Temp o t si ha F (t n )
T e T (t n )
(T e T 0 )
1
t n
n P er n ! 1 p Other x
n
t si ha
he x ! 1, e i si The following is the list of the al Limit I’m not sure. Oil and gas Lime x! 1
1 + 1 x
x
e : In fact, F (t)
T e T (t)
Lime x! 1 (T e T 0 )
1 + 1 x
t x
(T e T 0 ) Lime x! 1
1 + 1 x
x
t
(T e T 0 ) e
t
Topic: Thermodynamics Metodi: Differential Equations, Approximation & Series Expansion, Calculus-Integration Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Quesito n. 6. Il temp o aratteristi o del pro esso
e dato dalla ostan te temp o
= 1=
= C =K
3:7
10 3 s. La temp eratura dell’appartamen to dop o un’ora (o vv ero p er t
3600 s) risulta quindi T (t)
T e (T e T 0 ) e t=
= 26:7 Æ C PROBLEMA n. 4 { Una misura al volo. 50 Pun ti
Topic: Thermodynamics, Conservation of Energy Metodi: Differential Equations, Calculus-Integration, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Question No n. 6. Il Temp o characteristics or of the for It
e given from Other te Temp o
= 1=
= C =K
3:7
10 3 s. La Temp Other of the apartment to after o an hour (o vv I was p er t
3600 s) The following is the list of the So, what do you mean? T (t)
T e (T e T 0 ) e t=
= 26:7 Æ C The problem n. 4 { One of them. Measure al I’m going to fly. 50 The Commission ti
Topic: Thermodynamics, Conservation of Energy Metodi: Differential Equations, Calculus-Integration, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Heat Engine Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Quesito n. 1. P oi h
e il amp o elettri o
e uniforme, la forza
he agis e su un elettrone (o su uno ione)
e ostan te, di mo dulo pari a eE ; inoltre il moto a vviene nella direzione e nel v erso del amp o. In un generi o istan te t < t e ias un elettrone a vr a p er orso una distanza v e t. Ne segue
he il la v oro fatto su un singolo elettrone, in funzione del temp o, risulta: L e
eE v e t Un’espressione analoga v ale o vviamen te p er gli ioni.
Topic: Electrostatics, Modern-Quantum Physics Metodi: Kinematic Equations, Free-Body Diagram, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Question No n. 1. P oi h
e il amp o electrical or
e uniforms, la
- What ?
he the following: su un Electron (o su One of them. (i) the
e Other te, di mo Other equal a eE ; In addition il Motorcycles a He ‘s coming . In the Direction e In the v Other of the amp o. In un the genus or Other te t < t e The Commission shall adopt a decision on the Electron a vr a p Other One of them. distance v e t. Ne follows
he il la v gold made su un single the electron, in function of the Temp o, It is: L e
eE v e t A word Other v Other o I’m going to go. te p er The Commission I’m not going to lie.
Topic: Electrostatics, Modern-Quantum Physics Metodi: Kinematic Equations, Free-Body Diagram, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Quesito n. 2. P oi h
e il riv elatore pu o essere onsiderato ome un ondensatore isolato, l’energia o orren te p er far migrare elettroni e ioni viene prelev ata da quella immagazzinata nel ondensatore. P otremo dunque s riv ere: 1 2 C V 2 0
N eE v i t + N eE v e t + 1 2 C V 2
Da qui: 1 2 C (V 2 0 V 2
)
N eE (v i + v e ) t 1 2 C (V 0 + V
)(V 0 V
)
1 2 C (V 0 + V
) V (t)
N e V
d (v i + v e ) t P oi h
e il segnale V (t)
e molto minore di V 0 , p otremo p orre, on buona approssimazione, V
= V 0 nell’espressione pre eden te, ottenendo in ne: V (t)
N e C d (v i + v e ) t P ag. 5 AIF { Olimpiadi di Fisi a Ga ra Nazionale: SOLUZIONE della Prova T eo ri a { Senigallia { 18 Ap rile 2007
Topic: Electrostatics, Modern-Quantum Physics Metodi: Energy Conservation Method, Electric Potential Method, Approximation & Series Expansion Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Question No n. 2. P oi h
e il The following is the list of the countries of the European Union: Other, of a kind used for the manufacture of goods pu o to be Unseeded human beings un Other, of a kind used for the manufacture of goods the insulated energy o Other articles te p er
- to make migration Electrons e Other He ‘s coming . the following: Other da That one. Stored In the The wave-switching device. P Other So, what? The following is the list of the were: 1 2 C V 2 0 = N eE v i t
N eE v e t + 1 2 C V 2
Da Here it is: 1 2 C (V 2 0 V 2
)
N eE (v i + v e ) t 1 2 C (V 0 + V
)(V 0 V
)
1 2 C (V 0 + V
) V (t)
N e V
d (v i + v e ) t P oi h
e il Signal V (t)
e Very much Minor di V 0 , p Other p The horror, on Good . the approximation, V
= V 0 in the expression for Eden te, by obtaining in ne: V (t)
N e C d (v i + v e ) t P ag. 5 The following information is provided: { The Olympics di The following is a list of Ga ra National team: The Commission of the Try it . T eo ri a { The following is the list of countries: { 18 Ap Reels 2007
Topic: Electrostatics, Modern-Quantum Physics Metodi: Energy Conservation Method, Electric Potential Method, Approximation & Series Expansion Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.5 Soluzione: Soluzioni (PDF)
Quesito n. 3. Nell’istan te t e
x=v e gli elettroni raggiungono l’ano do, e da quel momen to in p oi non assorb ono pi
u energia. Il segnale V res e an ora, ma on tribuis ono solamen te gli ioni: V (t)
N e C d (v i t + x)
Topic: Electrostatics, Modern-Quantum Physics Metodi: Kinematic Equations, Physical Modeling, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)
Question No n. 3. In the Istan te t e
x=v e The Commission Electrons They reach the anus do, e da That one. Moments to in p oi Not Other, of a kind used for the manufacture of goods The Commission pi
u energy. Il Signal V Res and I’m going to be here. ma on The following table shows the results of the survey: Other te The Commission Other: V (t)
N e C d (v i t + x)
Topic: Electrostatics, Modern-Quantum Physics Metodi: Kinematic Equations, Physical Modeling, Energy Conservation Method Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)
Quesito n. 4. All’istan te t i
(d x)=v i gli ioni raggiungono il ato do. A quel pun to il segnale div en ta: V (t)
N e C d (d x + x)
N e C Come si pu o v edere, il v alore
nale dip ende solamen te dalla apa it a del ondensatore e dal n umero di oppie elettroni{ioni pro dotte dal passaggio della parti ella ionizzan te. Si noti
he a questo risultato si pu o arriv are molto fa ilmen te osserv ando
he, dop o
he tutta la ari a \pro dotta” dalla ionizzazione,
e stata ra olta, la ari a sulle armature dimin uis e di una quan tit a N e, e il p otenziale V 0 dimin uis e di una quan tit a N e=C .
Topic: Electrostatics, Modern-Quantum Physics Metodi: Electric Potential Method, Physical Modeling, Conservation Laws Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)
Question No n. 4. In the Republic of Kazakhstan te t i
(d x)=v i The Commission Other They reach il the act do. A That one. the following points are added: to il Signal Div en ta: V (t)
N e C d (d x + x)
N e C How si pu o v the following: il v Other
The Commission shall adopt a decision on the Dip Other Other te from
- What? a of the Other, of a kind used for the manufacture of goods e from n Other di Other Electrons for The Commission shall adopt implementing acts. from Passage of the She’s gone. Ionized te. Si Notes
he a This one. result si pu o I ‘m coming are Very much It’s a pain. te See also I ‘m going
he, after o
he All of them la the following points are inserted: The Commission ‘The first of these is the from ionization,
e It was The Commission shall adopt the following measures: la the following points are inserted: on the Other articles of iron or steel Minimum number of days Uis and di One of them. When Title a N e, e il p The following information shall be provided: V 0 Minimum number of days Uis and di One of them. When Title a N e=C .
Topic: Electrostatics, Modern-Quantum Physics Metodi: Electric Potential Method, Physical Modeling, Conservation Laws Competenze: Mathematical Modeling, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)
Quesito n. 5. Il gra o qualitativ o del segnale ra olto dal riv elatore risulta allora: 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” VENEZIA MESTRE fax: 041.584.1272 e-mail: olifis libero.i t P ag. 6
Topic: Electrostatics, Modern-Quantum Physics Metodi: Physical Modeling, Kinematic Equations Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)
Question No n. 5. Il The following is the list of the o The quality o of the Signal The Commission shall adopt a decision on the from The following is the list of the countries of the European Union: Other, of a kind used for the manufacture of goods The following is the list of the Then: 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 ‘R’ The Commission The Master The fax: 041.584.1272 E-mail: Free olive oil t P ag. 6
Topic: Electrostatics, Modern-Quantum Physics Metodi: Physical Modeling, Kinematic Equations Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Capacitor, Electron, Point Charge Fonte: Testo (PDF) — p.6 Soluzione: Soluzioni (PDF)